Authors: | Type: |

### 2018

- M. Berta, F. G. Brandao, J. Haegeman, V. B. Scholz, and F. Verstraete, “Thermal states as convex combinations of matrix product states,” PHYSICAL REVIEW B, vol. 98, iss. 23, p. 8, 2018.

[Bibtex]`@article{8588531, abstract = {We study thermal states of strongly interacting quantum spin chains and prove that those can be represented in terms of convex combinations of matrix product states. Apart from revealing new features of the entanglement structure of Gibbs states, our results provide a theoretical justification for the use of White's algorithm of minimally entangled typical thermal states. Furthermore, we shed new light on time dependent matrix product state algorithms which yield hydrodynamical descriptions of the underlying dynamics.}, articleno = {235154}, author = {Berta, Mario and Brandao, Fernando GSL and Haegeman, Jutho and Scholz, Volkher B and Verstraete, Frank}, issn = {2469-9950}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {23}, pages = {8}, title = {Thermal states as convex combinations of matrix product states}, url = {http://dx.doi.org/10.1103/PhysRevB.98.235154}, volume = {98}, year = {2018}, }`

- N. Bultinck, R. Vanhove, J. Haegeman, and F. Verstraete, “Global anomaly detection in two-dimensional symmetry-protected topological phases,” PHYSICAL REVIEW LETTERS, vol. 120, iss. 15, p. 6, 2018.

[Bibtex]`@article{8559938, abstract = {Edge theories of symmetry-protected topological phases are well known to possess global symmetry anomalies. In this Letter we focus on two-dimensional bosonic phases protected by an on-site symmetry and analyze the corresponding edge anomalies in more detail. Physical interpretations of the anomaly in terms of an obstruction to orbifolding and constructing symmetry-preserving boundaries are connected to the cohomology classification of symmetry-protected phases in two dimensions. Using the tensor network and matrix product state formalism we numerically illustrate our arguments and discuss computational detection schemes to identify symmetry-protected order in a ground state wave function.}, articleno = {156601}, author = {Bultinck, Nick and Vanhove, Robijn and Haegeman, Jutho and Verstraete, Frank}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {15}, pages = {6}, title = {Global anomaly detection in two-dimensional symmetry-protected topological phases}, url = {http://dx.doi.org/10.1103/PhysRevLett.120.156601}, volume = {120}, year = {2018}, }`

- V. Zauner-Stauber, L. Vanderstraeten, J. Haegeman, I. McCulloch, and F. Verstraete, “Topological nature of spinons and holons : elementary excitations from matrix product states with conserved symmetries,” PHYSICAL REVIEW B, vol. 97, iss. 23, p. 15, 2018.

[Bibtex]`@article{8570364, abstract = {We develop variational matrix product state (MPS) methods with symmetries to determine dispersion relations of one-dimensional quantum lattices as a function of momentum and preset quantum number. We test our methods on the XXZ spin chain, the Hubbard model, and a nonintegrable extended Hubbard model and determine the excitation spectra with a precision similar to the one of the ground state. The formulation in terms of quantum numbers makes the topological nature of spinons and holons very explicit. In addition, the method also enables an easy and efficient direct calculation of the necessary magnetic field or chemical potential required for a certain ground state magnetization or particle density.}, articleno = {235155}, author = {Zauner-Stauber, V and Vanderstraeten, Laurens and Haegeman, Jutho and McCulloch, IP and Verstraete, Frank}, issn = {2469-9950}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {23}, pages = {15}, title = {Topological nature of spinons and holons : elementary excitations from matrix product states with conserved symmetries}, url = {http://dx.doi.org/10.1103/PhysRevB.97.235155}, volume = {97}, year = {2018}, }`

- N. Bultinck, D. J. Williamson, J. Haegeman, and F. Verstraete, “Fermionic projected entangled-pair states and topological phases,” JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, vol. 51, iss. 2, p. 41, 2018.

[Bibtex]`@article{8556824, abstract = {We study fermionic matrix product operator algebras and identify the associated algebraic data. Using this algebraic data we construct fermionic tensor network states in two dimensions that have non-trivial symmetry-protected or intrinsic topological order. The tensor network states allow us to relate physical properties of the topological phases to the underlying algebraic data. We illustrate this by calculating defect properties and modular matrices of supercohomology phases. Our formalism also captures Majorana defects as we show explicitly for a class of \${\textbackslash}mathbb\{Z\}\_2\$ symmetry-protected and intrinsic topological phases. The tensor networks states presented here are well-suited for numerical applications and hence open up new possibilities for studying interacting fermionic topological phases.}, articleno = {025202}, author = {Bultinck, Nick and Williamson, Dominic J and Haegeman, Jutho and Verstraete, Frank}, issn = {1751-8113}, journal = {JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL}, language = {eng}, number = {2}, pages = {41}, title = {Fermionic projected entangled-pair states and topological phases}, url = {http://dx.doi.org/10.1088/1751-8121/aa99cc}, volume = {51}, year = {2018}, }`

- M. Fishman, L. Vanderstraeten, V. Zauner-Stauber, J. Haegeman, and F. Verstraete, “Faster methods for contracting infinite two-dimensional tensor networks,” PHYSICAL REVIEW B, vol. 98, iss. 23, p. 17, 2018.

[Bibtex]`@article{8588534, abstract = {We revisit the corner transfer matrix renormalization group (CTMRG) method of Nishino and Okunishi for contracting two-dimensional (2D) tensor networks and demonstrate that its performance can be substantially improved by determining the tensors using an eigenvalue solver as opposed to the power method used in CTMRG. We also generalize the variational uniform matrix product state (VUMPS) ansatz for diagonalizing 1D quantum Hamiltonians to the case of 2D transfer matrices and discuss similarities with the corner methods. These two new algorithms will be crucial to improving the performance of variational infinite projected entangled pair state (PEPS) methods.}, articleno = {235148}, author = {Fishman, MT and Vanderstraeten, Laurens and Zauner-Stauber, V and Haegeman, Jutho and Verstraete, Frank}, issn = {2469-9950}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {23}, pages = {17}, title = {Faster methods for contracting infinite two-dimensional tensor networks}, url = {http://dx.doi.org/10.1103/PhysRevB.98.235148}, volume = {98}, year = {2018}, }`

- L. Vanderstraeten, B. Vanhecke, and F. Verstraete, “Residual entropies for three-dimensional frustrated spin systems with tensor networks,” PHYSICAL REVIEW E, vol. 98, iss. 4, p. 8, 2018.

[Bibtex]`@article{8582922, abstract = {We develop a technique for calculating three-dimensional classical partition functions using projected entangled-pair states (PEPS). Our method is based on variational PEPS optimization algorithms for two-dimensional quantum spin systems, and allows us to compute free energies directly in the thermodynamic limit. The main focus of this work is classical frustration in three-dimensional many-body systems leading to an extensive ground-state degeneracy. We provide high-accuracy results for the residual entropy of the dimer model on the cubic lattice, water ice I-h, and water ice I-c. In addition, we show that these systems are in a Coulomb phase by computing the dipolar form of the correlation functions. As a further benchmark of our methods, we calculate the critical temperature and exponents of the Ising model on the cubic lattice.}, articleno = {042145}, author = {Vanderstraeten, Laurens and Vanhecke, Bram and Verstraete, Frank}, issn = {2470-0045}, journal = {PHYSICAL REVIEW E}, language = {eng}, number = {4}, pages = {8}, title = {Residual entropies for three-dimensional frustrated spin systems with tensor networks}, url = {http://dx.doi.org/10.1103/PhysRevE.98.042145}, volume = {98}, year = {2018}, }`

- L. Vanderstraeten, M. Van Damme, H. P. Buechler, and F. Verstraete, “Quasiparticles in quantum spin chains with long-range interactions,” PHYSICAL REVIEW LETTERS, vol. 121, iss. 9, p. 6, 2018.

[Bibtex]`@article{8575091, abstract = {We study quasiparticle excitations for quantum spin chains with long-range interactions using variational matrix product state techniques. It is confirmed that the local quasiparticle ansatz is able to capture those excitations very accurately, even when the correlation length becomes very large and in the case of topological nontrivial excitation such as spinons. It is demonstrated that the breaking of the Lieb-Robinson bound follows from the appearance of cusps in the dispersion relation, and evidence is given for a crossover between different quasiparticles as the long-range interactions are tuned.}, articleno = {090603}, author = {Vanderstraeten, Laurens and Van Damme, Maarten and Buechler, Hans Peter and Verstraete, Frank}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {9}, pages = {6}, title = {Quasiparticles in quantum spin chains with long-range interactions}, url = {http://dx.doi.org/10.1103/PhysRevLett.121.090603}, volume = {121}, year = {2018}, }`

- M. Bal, “Real-space renormalization group methods in the age of tensor network states,” PhD Thesis, 2018.

[Bibtex]`@phdthesis{8550528, abstract = {This dissertation contributes to the ongoing effort of understanding the origins and applications of real-space renormalization group methods in tensor network representations of classical and quantum many-body systems. First, we construct a matrix product operator ansatz to coarse-grain real-space transfer matrices of matrix product state descriptions of one-dimensional quantum spin chains. By treating the physical spin as an impurity, we unravel the virtual entanglement degrees of freedom of matrix product states into a layered structure to reveal an inherent renormalization group scale. Secondly, we rephrase tensor network renormalization for two-dimensional classical lattice models in a manifestly nonnegative way. The resulting real-space renormalization group flow preserves positivity and hence yields an interpretation in terms of Hamiltonian flows, reconciling modern real-space tensor network renormalization methods with traditional block-spin approaches. Thirdly, we study non-local symmetries in tensor networks by expressing two-dimensional classical partition functions in terms of strange correlators of judiciously chosen product states and string-net wave functions. We exhibit and exploit the emerging non-local symmetries of the partition function at criticality and highlight parallels between topological sectors and conformal primary fields in the shared framework of matrix product operator symmetries. Additionally, we provide a complementary perspective on real-space renormalization by recognizing known tensor network renormalization methods as the approximate truncation of an exactly coarse-grained strange correlator.}, author = {Bal, Matthias}, language = {eng}, pages = {X, 208}, publisher = {Ghent University. Faculty of Sciences}, school = {Ghent University}, title = {Real-space renormalization group methods in the age of tensor network states}, year = {2018}, }`

- R. Vanhove, M. Bal, D. J. Williamson, N. Bultinck, J. Haegeman, and F. Verstraete, “Mapping topological to conformal field theories through strange correlators,” PHYSICAL REVIEW LETTERS, vol. 121, iss. 17, p. 6, 2018.

[Bibtex]`@article{8582918, abstract = {We extend the concept of strange correlators, defined for symmetry-protected phases in You et al. [Phys. Rev. Lett. 112, 247202 (2014)], to topological phases of matter by taking the inner product between string-net ground states and product states. The resulting two-dimensional partition functions are shown to be either critical or symmetry broken, since the corresponding transfer matrices inherit all matrix product operator symmetries of the string-net states. For the case of critical systems, these nonlocal matrix product operator symmetries are the lattice remnants of topological conformal defects in the field theory description. Following Aasen et al. [J. Phys. A 49, 354001 (2016)], we argue that the different conformal boundary conditions can be obtained by applying the strange correlator concept to the different topological sectors of the string net obtained from Ocneanu's tube algebra. This is demonstrated on the lattice by calculating the conformal field theory spectra in the different topological sectors for the Fibonacci (hard-hexagon) and Ising string net. Additionally, we provide a complementary perspective on symmetry-preserving real-space renormalization by showing how known tensor network renormalization methods can be understood as the approximate truncation of an exactly coarse-grained strange correlator.}, articleno = {177203}, author = {Vanhove, Robijn and Bal, Matthias and Williamson, Dominic J and Bultinck, Nick and Haegeman, Jutho and Verstraete, Frank}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {17}, pages = {6}, title = {Mapping topological to conformal field theories through strange correlators}, url = {http://dx.doi.org/10.1103/PhysRevLett.121.177203}, volume = {121}, year = {2018}, }`

- K. Gunst, F. Verstraete, S. Wouters, Ö. Legeza, and D. Van Neck, “T3NS : three-legged tree tensor network states,” JOURNAL OF CHEMICAL THEORY AND COMPUTATION, vol. 14, iss. 4, pp. 2026-2033, 2018.

[Bibtex]`@article{8560735, abstract = {We present a new variational tree tensor network state (TTNS) ansatz, the three-legged tree tensor network state (T3NS). Physical tensors are interspersed with branching tensors. Physical tensors have one physical index and at most two virtual indices, as in the matrix product state (MPS) ansatz of the density matrix renormalization group (DMRG). Branching tensors have no physical index, but up to three virtual indices. In this way, advantages of DMRG, in particular a low computational cost and a simple implementation of symmetries, are combined with advantages of TTNS, namely incorporating more entanglement. Our code is capable of simulating quantum chemical Hamiltonians, and we present several proof-of principle calculations on LiF, N-2, and the bis(mu-oxo) and mu-eta(2):eta(2) peroxo isomers of [Cu2O2](2+).}, author = {Gunst, Klaas and Verstraete, Frank and Wouters, Sebastian and Legeza, {\"O}rs and Van Neck, Dimitri}, issn = {1549-9618}, journal = {JOURNAL OF CHEMICAL THEORY AND COMPUTATION}, language = {eng}, number = {4}, pages = {2026--2033}, title = {T3NS : three-legged tree tensor network states}, url = {http://dx.doi.org/10.1021/acs.jctc.8b00098}, volume = {14}, year = {2018}, }`

- V. Zauner-Stauber, L. Vanderstraeten, M. Fishman, F. Verstraete, and J. Haegeman, “Variational optimization algorithms for uniform matrix product states,” PHYSICAL REVIEW B, vol. 97, iss. 4, p. 31, 2018.

[Bibtex]`@article{8555700, abstract = {We combine the density matrix renormalization group (DMRG) with matrix product state tangent space concepts to construct a variational algorithm for finding ground states of one-dimensional quantum lattices in the thermodynamic limit. A careful comparison of this variational uniform matrix product state algorithm (VUMPS) with infinite density matrix renormalization group (IDMRG) and with infinite time evolving block decimation (ITEBD) reveals substantial gains in convergence speed and precision. We also demonstrate that VUMPS works very efficiently for Hamiltonians with long-range interactions and also for the simulation of two-dimensional models on infinite cylinders. The new algorithm can be conveniently implemented as an extension of an already existing DMRG implementation.}, articleno = {045145}, author = {Zauner-Stauber, V and Vanderstraeten, Laurens and Fishman, MT and Verstraete, Frank and Haegeman, Jutho}, issn = {2469-9950}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {4}, pages = {31}, title = {Variational optimization algorithms for uniform matrix product states}, url = {http://dx.doi.org/10.1103/PhysRevB.97.045145}, volume = {97}, year = {2018}, }`

### 2017

- J. Cirac, D. Perez-Garcia, N. Schuch, and F. Verstraete, “Matrix product density operators : renormalization fixed points and boundary theories,” ANNALS OF PHYSICS, vol. 378, pp. 100-149, 2017.

[Bibtex]`@article{8525790, author = {Cirac, JI and Perez-Garcia, D and Schuch, N and Verstraete, Frank}, issn = {0003-4916}, journal = {ANNALS OF PHYSICS}, language = {eng}, pages = {100--149}, title = {Matrix product density operators : renormalization fixed points and boundary theories}, url = {http://dx.doi.org/10.1016/j.aop.2016.12.030}, volume = {378}, year = {2017}, }`

- N. Bultinck, “Tensor network states and topological quantum phases,” PhD Thesis, 2017.

[Bibtex]`@phdthesis{8541337, author = {Bultinck, Nick}, language = {eng}, pages = {261}, publisher = {Ghent University. Faculty of Sciences}, school = {Ghent University}, title = {Tensor network states and topological quantum phases}, year = {2017}, }`

- I. J. Cirac, D. Perez-Garcia, N. Schuch, and F. Verstraete, “Matrix product unitaries : structure, symmetries, and topological invariants,” JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, p. 37, 2017.

[Bibtex]`@article{8530943, abstract = {Matrix product vectors form the appropriate framework to study and classify one-dimensional quantum systems. In this work, we develop the structure theory of matrix product unitary operators (MPUs) which appear e.g. in the description of time evolutions of one-dimensional systems. We prove that all MPUs have a strict causal cone, making them quantum cellular automata (QCAs), and derive a canonical form for MPUs which relates different MPU representations of the same unitary through a local gauge. We use this canonical form to prove an index theorem for MPUs which gives the precise conditions under which two MPUs are adiabatically connected, providing an alternative derivation to that of (Gross et al 2012 Commun. Math. Phys. 310 419) for QCAs. We also discuss the effect of symmetries on the MPU classification. In particular, we characterize the tensors corresponding to MPU that are invariant under conjugation, time reversal, or transposition. In the first case, we give a full characterization of all equivalence classes. Finally, we give several examples of MPU possessing different symmetries.}, articleno = {083105}, author = {Cirac, J Ignacio and Perez-Garcia, David and Schuch, Norbert and Verstraete, Frank}, issn = {1742-5468}, journal = {JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT}, language = {eng}, pages = {37}, title = {Matrix product unitaries : structure, symmetries, and topological invariants}, url = {http://dx.doi.org/10.1088/1742-5468/aa7e55}, year = {2017}, }`

- D. Draxler, J. Haegeman, F. Verstraete, and M. Rizzi, “Continuous matrix product states with periodic boundary conditions and an application to atomtronics,” PHYSICAL REVIEW B, vol. 95, iss. 4, p. 14, 2017.

[Bibtex]`@article{8520758, abstract = {We introduce a time evolution algorithm for one-dimensional quantum field theories with periodic boundary conditions. This is done by applying the Dirac-Frenkel time-dependent variational principle to the set of translational invariant continuous matrix product stateswith periodic boundary conditions. Moreover, the ansatz is accompanied with additional boundary degrees of freedom to study quantum impurity problems. The algorithm allows for a cutoff in the spectrum of the transfer matrix and thus has an efficient computational scaling. In particular we study the prototypical example of an atomtronic system-an interacting Bose gas rotating in a ring shaped trap in the presence of a localized barrier potential.}, articleno = {045145}, author = {Draxler, Damian and Haegeman, Jutho and Verstraete, Frank and Rizzi, Matteo}, issn = {2469-9950}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {4}, pages = {14}, title = {Continuous matrix product states with periodic boundary conditions and an application to atomtronics}, url = {http://dx.doi.org/10.1103/PhysRevB.95.045145}, volume = {95}, year = {2017}, }`

- N. Bultinck, M. Mariën, D. Williamson, M. c{S}ahinou{g}lu, J. Haegeman, and F. Verstraete, “Anyons and matrix product operator algebras,” ANNALS OF PHYSICS, vol. 378, pp. 183-233, 2017.

[Bibtex]`@article{8519065, author = {Bultinck, Nick and Mari{\"e}n, Micha{\"e}l and Williamson, DJ and \c{S}ahino\u{g}lu, MB and Haegeman, Jutho and Verstraete, Frank}, issn = {0003-4916}, journal = {ANNALS OF PHYSICS}, language = {eng}, pages = {183--233}, title = {Anyons and matrix product operator algebras}, url = {http://dx.doi.org/10.1016/j.aop.2017.01.004}, volume = {378}, year = {2017}, }`

- N. Bultinck, D. J. Williamson, J. Haegeman, and F. Verstraete, “Fermionic matrix product states and one-dimensional topological phases,” PHYSICAL REVIEW B, vol. 95, iss. 7, p. 24, 2017.

[Bibtex]`@article{8518864, abstract = {We develop the formalism of fermionic matrix product states (fMPS) and show how irreducible fMPS fall in two different classes, related to the different types of simple Z(2) graded algebras, which are physically distinguished by the absence or presence of Majorana edge modes. The local structure of fMPS with Majorana edge modes also implies that there is always a twofold degeneracy in the entanglement spectrum. Using the fMPS formalism, we make explicit the correspondence between the Z(8) classification of time-reversal-invariant spinless superconductors and the modulo 8 periodicity in the representation theory of real Clifford algebras. Studying fMPS with general onsite unitary and antiunitary symmetries allows us to define invariants that label symmetry-protected phases of interacting fermions. The behavior of these invariants under stacking of fMPS is derived, which reveals the group structure of such interacting phases. We also consider spatial symmetries and show how the invariant phase factor in the partition function of reflection-symmetric phases on an unorientable manifold appears in the fMPS framework.}, articleno = {075108}, author = {Bultinck, Nick and Williamson, Dominic J and Haegeman, Jutho and Verstraete, Frank}, issn = {2469-9950}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {7}, pages = {24}, title = {Fermionic matrix product states and one-dimensional topological phases}, url = {http://dx.doi.org/10.1103/PhysRevB.95.075108}, volume = {95}, year = {2017}, }`

- K. Duivenvoorden, M. Iqbal, J. Haegeman, F. Verstraete, and N. Schuch, “Entanglement phases as holographic duals of anyon condensates,” PHYSICAL REVIEW B, vol. 95, iss. 23, p. 24, 2017.

[Bibtex]`@article{8525439, abstract = {Anyon condensation forms a mechanism that allows us to relate different topological phases. We study anyon condensation in the framework of projected entangled pair states (PEPS) where topological order is characterized through local symmetries of the entanglement. We show that anyon condensation is in one-to-one correspondence to the behavior of the virtual entanglement state at the boundary (i.e., the entanglement spectrum) under those symmetries, which encompasses both symmetry breaking and symmetry protected (SPT) order, and we use this to characterize all anyon condensations for Abelian double models through the structure of their entanglement spectrum. We illustrate our findings with the Z(4) double model, which can give rise to both toric code and doubled semion order through condensation, distinguished by the SPT structure of their entanglement. Using the ability of our framework to directly measure order parameters for condensation and deconfinement, we numerically study the phase diagram of the model, including direct phase transitions between the doubled semion and the toric code phase, which are not described by anyon condensation.}, articleno = {235119}, author = {Duivenvoorden, Kasper and Iqbal, Mohsin and Haegeman, Jutho and Verstraete, Frank and Schuch, Norbert}, issn = {2469-9950}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {23}, pages = {24}, title = {Entanglement phases as holographic duals of anyon condensates}, url = {http://dx.doi.org/10.1103/PhysRevB.95.235119}, volume = {95}, year = {2017}, }`

- M. Bal, M. Mariën, J. Haegeman, and F. Verstraete, “Renormalization group flows of Hamiltonians using tensor networks,” PHYSICAL REVIEW LETTERS, vol. 118, iss. 25, p. 5, 2017.

[Bibtex]`@article{8525054, abstract = {A renormalization group flow of Hamiltonians for two-dimensional classical partition functions is constructed using tensor networks. Similar to tensor network renormalization [G. Evenbly and G. Vidal, Phys. Rev. Lett. 115, 180405 (2015); S. Yang, Z.-C. Gu, and X.-G. Wen, Phys. Rev. Lett. 118, 110504 (2017)], we obtain approximate fixed point tensor networks at criticality. Our formalism, however, preserves positivity of the tensors at every step and hence yields an interpretation in terms of Hamiltonian flows. We emphasize that the key difference between tensor network approaches and Kadanoff{\textquoteright}s spin blocking method can be understood in terms of a change of the local basis at every decimation step, a property which is crucial to overcome the area law of mutual information. We derive algebraic relations for fixed point tensors, calculate critical exponents, and benchmark our method on the Ising model and the six-vertex model.}, articleno = {250602}, author = {Bal, Matthias and Mari{\"e}n, Micha{\"e}l and Haegeman, Jutho and Verstraete, Frank}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {25}, pages = {5}, title = {Renormalization group flows of Hamiltonians using tensor networks}, url = {http://dx.doi.org/10.1103/PhysRevLett.118.250602}, volume = {118}, year = {2017}, }`

- J. Haegeman, D. Draxler, V. Stojevic, I. J. Cirac, T. J. Osborne, and F. Verstraete, “Quantum Gross-Pitaevskii equation,” SCIPOST PHYSICS, vol. 3, iss. 1, p. 18, 2017.

[Bibtex]`@article{8534838, abstract = {We introduce a non-commutative generalization of the Gross-Pitaevskii equation for one-dimensional quantum gasses and quantum liquids. This generalization is obtained by applying the time-dependent variational principle to the variational manifold of continuous matrix product states. This allows for a full quantum description of many body system - including entanglement and correlations-and thus extends significantly beyond the usual mean-field description of the Gross-Pitaevskii equation, which is known to fail for (quasi) one-dimensional systems. By linearizing around a stationary solution, we furthermore derive an associated generalization of the Bogoliubov - de Gennes equations. This framework is applied to compute the steady state response amplitude to a periodic perturbation of the potential.}, articleno = {006}, author = {Haegeman, Jutho and Draxler, Damian and Stojevic, Vid and Cirac, J Ignacio and Osborne, Tobias J and Verstraete, Frank}, issn = {2542-4653}, journal = {SCIPOST PHYSICS}, language = {eng}, number = {1}, pages = {18}, title = {Quantum Gross-Pitaevskii equation}, url = {http://dx.doi.org/10.21468/SciPostPhys.3.1.006}, volume = {3}, year = {2017}, }`

- M. Mariën, J. Haegeman, P. Fendley, and F. Verstraete, “Condensation-driven phase transitions in perturbed string nets,” PHYSICAL REVIEW B, vol. 96, iss. 15, p. 9, 2017.

[Bibtex]`@article{8536702, abstract = {We develop methods to probe the excitation spectrum of topological phases of matter in two spatial dimensions. Applying these to the Fibonacci string nets perturbed away from exact solvability, we analyze a topological phase transition driven by the condensation of non-Abelian anyons. Our numerical results illustrate how such phase transitions involve the spontaneous breaking of a topological symmetry, generalizing the traditional Landau paradigm. The main technical tool is the characterization of the ground states using tensor networks and the topological properties using matrix-product-operator symmetries. The topological phase transition manifests itself by symmetry breaking in the entanglement degrees of freedom of the quantum transfer matrix.}, articleno = {155127}, author = {Mari{\"e}n, Micha{\"e}l and Haegeman, Jutho and Fendley, Paul and Verstraete, Frank}, issn = {2469-9950}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {15}, pages = {9}, title = {Condensation-driven phase transitions in perturbed string nets}, url = {http://dx.doi.org/10.1103/PhysRevB.96.155127}, volume = {96}, year = {2017}, }`

- J. Haegeman and F. Verstraete, “Diagonalizing transfer matrices and matrix product operators : a medley of exact and computational methods,” Annual Review of Condensed Matter Physics, vol. 8, pp. 355-406, 2017.

[Bibtex]`@article{8519063, abstract = {Transfer matrices and matrix product operators play a ubiquitous role in the field of many-body physics. This review gives an idiosyncratic overview of applications, exact results, and computational aspects of diagonalizing transfer matrices and matrix product operators. The results in this paper are a mixture of classic results, presented from the point of view of tensor networks, and new results. Topics discussed are exact solutions of transfer matrices in equilibrium and nonequilibrium statistical physics, tensor network states, matrix product operator algebras, and numerical matrix product state methods for finding extremal eigenvectors of matrix product operators.}, author = {Haegeman, Jutho and Verstraete, Frank}, editor = {Marchetti, MC and Sachdev, S}, isbn = {9780824350086}, issn = {1947-5454}, journal = {Annual Review of Condensed Matter Physics}, language = {eng}, pages = {355--406}, publisher = {Annual Reviews}, title = {Diagonalizing transfer matrices and matrix product operators : a medley of exact and computational methods}, url = {http://dx.doi.org/10.1146/annurev-conmatphys-031016-025507}, volume = {8}, year = {2017}, }`

- L. Vanderstraeten, M. Mariën, J. Haegeman, N. Schuch, J. Vidal, and F. Verstraete, “Bridging perturbative expansions with tensor networks,” PHYSICAL REVIEW LETTERS, vol. 119, iss. 7, p. 6, 2017.

[Bibtex]`@article{8529771, abstract = {We demonstrate that perturbative expansions for quantum many-body systems can be rephrased in terms of tensor networks, thereby providing a natural framework for interpolating perturbative expansions across a quantum phase transition. This approach leads to classes of tensor-network states parametrized by few parameters with a clear physical meaning, while still providing excellent variational energies. We also demonstrate how to construct perturbative expansions of the entanglement Hamiltonian, whose eigenvalues form the entanglement spectrum, and how the tensor-network approach gives rise to order parameters for topological phase transitions.}, articleno = {070401}, author = {Vanderstraeten, Laurens and Mari{\"e}n, Micha{\"e}l and Haegeman, Jutho and Schuch, Norbert and Vidal, Julien and Verstraete, Frank}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {7}, pages = {6}, title = {Bridging perturbative expansions with tensor networks}, url = {http://dx.doi.org/10.1103/PhysRevLett.119.070401}, volume = {119}, year = {2017}, }`

- B. Buyens, S. Montangero, J. Haegeman, F. Verstraete, and K. Van Acoleyen, “Finite-representation approximation of lattice gauge theories at the continuum limit with tensor networks,” PHYSICAL REVIEW D, vol. 95, iss. 9, p. 23, 2017.

[Bibtex]`@article{8521403, abstract = {It has been established that matrix product states can be used to compute the ground state and single-particle excitations and their properties of lattice gauge theories at the continuum limit. However, by construction, in this formalism the Hilbert space of the gauge fields is truncated to a finite number of irreducible representations of the gauge group. We investigate quantitatively the influence of the truncation of the infinite number of representations in the Schwinger model, one-flavor QED 2, with a uniform electric background field. We compute the two-site reduced density matrix of the ground state and the weight of each of the representations. We find that this weight decays exponentially with the quadratic Casimir invariant of the representation which justifies the approach of truncating the Hilbert space of the gauge fields. Finally, we compute the single-particle spectrum of the model as a function of the electric background field.}, articleno = {094509}, author = {Buyens, Boye and Montangero, Simone and Haegeman, Jutho and Verstraete, Frank and Van Acoleyen, Karel}, issn = {2470-0010}, journal = {PHYSICAL REVIEW D}, language = {eng}, number = {9}, pages = {23}, title = {Finite-representation approximation of lattice gauge theories at the continuum limit with tensor networks}, url = {http://dx.doi.org/10.1103/PhysRevD.95.094509}, volume = {95}, year = {2017}, }`

- B. Buyens, J. Haegeman, F. Hebenstreit, F. Verstraete, and K. Van Acoleyen, “Real-time simulation of the Schwinger effect with matrix product states,” PHYSICAL REVIEW D, vol. 96, iss. 11, p. 15, 2017.

[Bibtex]`@article{8542584, abstract = {Matrix Product States (MPS) are used for the simulation of the real-time dynamics induced by an electric quench on the vacuum state of the massive Schwinger model. For small quenches it is found that the obtained oscillatory behavior of local observables can be explained from the single-particle excitations of the quenched Hamiltonian. For large quenches damped oscillations are found and comparison of the late time behavior with the appropriate Gibbs states seems to give some evidence for the onset of thermalization. Finally, the MPS real-time simulations are compared with results from real-time lattice gauge theory which are expected to agree in the limit of large quenches.}, articleno = {114501}, author = {Buyens, Boye and Haegeman, Jutho and Hebenstreit, Florian and Verstraete, Frank and Van Acoleyen, Karel}, issn = {2470-0010}, journal = {PHYSICAL REVIEW D}, language = {eng}, number = {11}, pages = {15}, title = {Real-time simulation of the Schwinger effect with matrix product states}, url = {http://dx.doi.org/10.1103/PhysRevD.96.114501}, volume = {96}, year = {2017}, }`

### 2016

- J. Haegeman, C. Lubich, I. Oseledets, B. Vandereycken, and F. Verstraete, “Unifying time evolution and optimization with matrix product states,” PHYSICAL REVIEW B, vol. 94, iss. 16, p. 10, 2016.

[Bibtex]`@article{8152454, abstract = {We show that the time-dependent variational principle provides a unifying framework for time-evolution methods and optimization methods in the context of matrix product states. In particular, we introduce a new integration scheme for studying time evolution, which can cope with arbitrary Hamiltonians, including those with long-range interactions. Rather than a Suzuki-Trotter splitting of the Hamiltonian, which is the idea behind the adaptive time-dependent density matrix renormalization group method or time-evolving block decimation, our method is based on splitting the projector onto the matrix product state tangent space as it appears in the Dirac-Frenkel time-dependent variational principle. We discuss how the resulting algorithm resembles the density matrix renormalization group (DMRG) algorithm for finding ground states so closely that it can be implemented by changing just a few lines of code and it inherits the same stability and efficiency. In particular, our method is compatible with any Hamiltonian for which ground-state DMRG can be implemented efficiently. In fact, DMRG is obtained as a special case of our scheme for imaginary time evolution with infinite time step.}, articleno = {165116}, author = {Haegeman, Jutho and Lubich, Christian and Oseledets, Ivan and Vandereycken, Bart and Verstraete, Frank}, issn = {2469-9950}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {16}, pages = {10}, title = {Unifying time evolution and optimization with matrix product states}, url = {http://dx.doi.org/10.1103/PhysRevB.94.165116}, volume = {94}, year = {2016}, }`

- M. Mariën, “The entanglement structure of topological quantum phases,” PhD Thesis, 2016.

[Bibtex]`@phdthesis{8173707, author = {Mari{\"e}n, Micha{\"e}l}, language = {eng}, pages = {XIV, 252}, publisher = {Ghent University. Faculty of Sciences}, school = {Ghent University}, title = {The entanglement structure of topological quantum phases}, year = {2016}, }`

- M. Mariën, K. Audenaert, K. Van Acoleyen, and F. Verstraete, “Entanglement rates and the stability of the area law for the entanglement entropy,” COMMUNICATIONS IN MATHEMATICAL PHYSICS, vol. 346, iss. 1, pp. 35-73, 2016.

[Bibtex]`@article{8152472, abstract = {We prove a conjecture by Bravyi on an upper bound on entanglement rates of local Hamiltonians. We then use this bound to prove the stability of the area law for the entanglement entropy of quantum spin systems under adiabatic and quasi-adiabatic evolutions.}, author = {Mari{\"e}n, Micha{\"e}l and Audenaert, Koenraad and Van Acoleyen, Karel and Verstraete, Frank}, issn = {0010-3616}, journal = {COMMUNICATIONS IN MATHEMATICAL PHYSICS}, language = {eng}, number = {1}, pages = {35--73}, title = {Entanglement rates and the stability of the area law for the entanglement entropy}, url = {http://dx.doi.org/10.1007/s00220-016-2709-5}, volume = {346}, year = {2016}, }`

- L. Vanderstraeten, J. Haegeman, P. Corboz, and F. Verstraete, “Gradient methods for variational optimization of projected entangled-pair states,” PHYSICAL REVIEW B, vol. 94, iss. 15, p. 14, 2016.

[Bibtex]`@article{8152448, abstract = {We present a conjugate-gradient method for the ground-state optimization of projected entangled-pair states (PEPS) in the thermodynamic limit, as a direct implementation of the variational principle within the PEPS manifold. Our optimization is based on an efficient and accurate evaluation of the gradient of the global energy functional by using effective corner environments, and is robust with respect to the initial starting points. It has the additional advantage that physical and virtual symmetries can be straightforwardly implemented. We provide the tools to compute static structure factors directly in momentum space, as well as the variance of the Hamiltonian. We benchmark our method on Ising and Heisenberg models, and show a significant improvement on the energies and order parameters as compared to algorithms based on imaginary-time evolution.}, articleno = {155123}, author = {Vanderstraeten, Laurens and Haegeman, Jutho and Corboz, Philippe and Verstraete, Frank}, issn = {2469-9950}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {15}, pages = {14}, title = {Gradient methods for variational optimization of projected entangled-pair states}, url = {http://dx.doi.org/10.1103/PhysRevB.94.155123}, volume = {94}, year = {2016}, }`

- M. Bal, M. M. Rams, V. Zauner, J. Haegeman, and F. Verstraete, “Matrix product state renormalization,” PHYSICAL REVIEW B, vol. 94, iss. 20, p. 14, 2016.

[Bibtex]`@article{8164817, abstract = {The truncation or compression of the spectrum of Schmidt values is inherent to the matrix product state (MPS) approximation of one-dimensional quantum ground states. We provide a renormalization group picture by interpreting this compression as an application of Wilson's numerical renormalization group along the imaginary time direction appearing in the path integral representation of the state. The location of the physical index is considered as an impurity in the transfer matrix and static MPS correlation functions are reinterpreted as dynamical impurity correlations. Coarse-graining the transfer matrix is performed using a hybrid variational ansatz based on matrix product operators, combining ideas of MPS and the multiscale entanglement renormalization ansatz. Through numerical comparison with conventional MPS algorithms, we explicitly verify the impurity interpretation of MPS compression, as put forward by V. Zauner et al. [New J. Phys. 17, 053002 (2015)] for the transverse-field Ising model. Additionally, we motivate the conceptual usefulness of endowing MPS with an internal layered structure by studying restricted variational subspaces to describe elementary excitations on top of the ground state, which serves to elucidate a transparent renormalization group structure ingrained in MPS descriptions of ground states.}, articleno = {205122}, author = {Bal, Matthias and Rams, Marek M and Zauner, Valentin and Haegeman, Jutho and Verstraete, Frank}, issn = {2469-9950}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {20}, pages = {14}, title = {Matrix product state renormalization}, url = {http://dx.doi.org/10.1103/PhysRevB.94.205122}, volume = {94}, year = {2016}, }`

- K. Van Acoleyen, N. Bultinck, J. Haegeman, M. Mariën, V. Scholz, and F. Verstraete, “Entanglement of distillation for lattice gauge theories,” PHYSICAL REVIEW LETTERS, vol. 117, iss. 13, p. 5, 2016.

[Bibtex]`@article{8152295, abstract = {We study the entanglement structure of lattice gauge theories from the local operational point of view, and, similar to Soni and Trivedi [J. High Energy Phys. 1 (2016) 1], we show that the usual entanglement entropy for a spatial bipartition can be written as the sum of an undistillable gauge part and of another part corresponding to the local operations and classical communication distillable entanglement, which is obtained by depolarizing the local superselection sectors. We demonstrate that the distillable entanglement is zero for pure Abelian gauge theories at zero gauge coupling, while it is in general nonzero for the non-Abelian case. We also consider gauge theories with matter, and show in a perturbative approach how area laws-including a topological correction-emerge for the distillable entanglement. Finally, we also discuss the entanglement entropy of gauge fixed states and show that it has no relation to the physical distillable entropy.}, articleno = {131602}, author = {Van Acoleyen, Karel and Bultinck, Nick and Haegeman, Jutho and Mari{\"e}n, Micha{\"e}l and Scholz, Volker and Verstraete, Frank}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {13}, pages = {5}, title = {Entanglement of distillation for lattice gauge theories}, url = {http://dx.doi.org/10.1103/PhysRevLett.117.131602}, volume = {117}, year = {2016}, }`

- V. Zauner, D. Draxler, L. Vanderstraeten, J. Haegeman, and F. Verstraete, “Symmetry breaking and the geometry of reduced density matrices,” NEW JOURNAL OF PHYSICS, vol. 18, p. 8, 2016.

[Bibtex]`@article{8513360, abstract = {The concept of symmetry breaking and the emergence of corresponding local order parameters constitute the pillars of modern day many body physics. We demonstrate that the existence of symmetry breaking is a consequence of the geometric structure of the convex set of reduced density matrices of all possible many body wavefunctions. The surfaces of these convex bodies exhibit non-analyticities, which signal the emergence of symmetry breaking and of an associated order parameter and also show different characteristics for different types of phase transitions. We illustrate this with three paradigmatic examples of many body systems exhibiting symmetry breaking: the quantum Ising model, the classical q-state Potts model in two-dimensions at finite temperature and the ideal Bose gas in three-dimensions at finite temperature. This state based viewpoint on phase transitions provides a unique novel tool for studying exotic many body phenomena in quantum and classical systems.}, articleno = {113033}, author = {Zauner, V and Draxler, D and Vanderstraeten, Laurens and Haegeman, Jutho and Verstraete, Frank}, issn = {1367-2630}, journal = {NEW JOURNAL OF PHYSICS}, language = {eng}, pages = {8}, title = {Symmetry breaking and the geometry of reduced density matrices}, url = {http://dx.doi.org/10.1088/1367-2630/18/11/113033}, volume = {18}, year = {2016}, }`

- L. Vanderstraeten, “Tensor network states and effective particles for low-dimensional quantum spin systems,” PhD Thesis, 2016.

[Bibtex]`@phdthesis{8501428, abstract = {In this dissertation the author develops new techniques for simulating the low-energy behaviour of quantum spin systems in one and two dimensions. These techniques arise through the combination of two themes in many-particle physics: (i) the concept of quasiparticles as the effective low-energy degrees of freedom in a condensed-matter system, and (ii) entanglement as the characteristic feature for describing quantum phases of matter. Whereas the former gave rise to the use of effective field theories for understanding many-particle systems, the latter led to the development of tensor network states as a description of the entanglement distribution in quantum low-energy states. Combining these developments, the author uses the formalism of tensor network states to derive an effective particle description for one- and two-dimensional spin systems that exhibit strong quantum correlations.}, author = {Vanderstraeten, Laurens}, language = {eng}, pages = {188}, publisher = {Ghent University. Faculty of Sciences}, school = {Ghent University}, title = {Tensor network states and effective particles for low-dimensional quantum spin systems}, year = {2016}, }`

- D. J. Williamson, N. Bultinck, M. Mariën, M. B. c{S}ahinou{g}lu, J. Haegeman, and F. Verstraete, “Matrix product operators for symmetry-protected topological phases : gauging and edge theories,” PHYSICAL REVIEW B, vol. 94, iss. 20, p. 32, 2016.

[Bibtex]`@article{8501634, abstract = {Projected entangled pair states (PEPS) provide a natural ansatz for the ground states of gapped, local Hamiltonians in which global characteristics of a quantum state are encoded in properties of local tensors. We develop a framework to describe onsite symmetries, as occurring in systems exhibiting symmetry-protected topological (SPT) quantum order, in terms of virtual symmetries of the local tensors expressed as a set of matrix product operators (MPOs) labeled by distinct group elements. These MPOs describe the possibly anomalous symmetry of the edge theory, whose local degrees of freedom are concretely identified in a PEPS. A classification of SPT phases is obtained by studying the obstructions to continuously deforming one set of MPOs into another, recovering the results derived for fixed-point models [Chen et al., Phys. Rev. B 87, 155114 (2013)]. Our formalism accommodates perturbations away from fixed-point models, opening the possibility of studying phase transitions between different SPT phases. We also demonstrate that applying the recently developed quantum state gauging procedure to a SPT PEPS yields a PEPS with topological order determined by the initial symmetry MPOs. The MPO framework thus unifies the different approaches to classifying SPT phases, via fixed-point models, boundary anomalies, or gauging the symmetry, into the single problem of classifying inequivalent sets of matrix product operator symmetries that are defined purely in terms of a PEPS.}, articleno = {205150}, author = {Williamson, Dominic J and Bultinck, Nick and Mari{\"e}n, Micha{\"e}l and \c{S}ahino\u{g}lu, Mehmet B and Haegeman, Jutho and Verstraete, Frank}, issn = {2469-9950}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {20}, pages = {32}, title = {Matrix product operators for symmetry-protected topological phases : gauging and edge theories}, url = {http://dx.doi.org/10.1103/PhysRevB.94.205150}, volume = {94}, year = {2016}, }`

- L. Wang, Z. Gu, F. Verstraete, and X. Wen, “Tensor-product state approach to spin-1/2 square J\unmatched2081-J\unmatched2082 antiferromagnetic Heisenberg model : evidence for deconfined quantum criticality,” PHYSICAL REVIEW B, vol. 94, iss. 7, p. 6, 2016.

[Bibtex]`@article{8152466, abstract = {The ground state phase of a spin-1/2 J(1)-J(2) antiferromagnetic Heisenberg model on a square lattice around the maximally frustrated regime (J(2) similar to 0.5J(1)) has been debated for decades. Here we study this model using the cluster update algorithm for tensor-product states (TPSs). The ground state energies at finite sizes and in the thermodynamic limit (with finite size scaling) are in good agreement with exact diagonalization study. Through finite size scaling of the spin correlation function, we find the critical point J(2)(c1) = 0.572(5) J(1) and critical exponents nu = 0.50(8), eta(s) = 0.28(6). In the range of 0.572 {\textlangle} J(2)/J(1) {\textlangle}= 0.6 we find a paramagnetic ground state with an exponentially decaying spin-spin correlation. Up to a 24x24 system size, we observe power law decaying dimer-dimer and plaquette-plaquette correlations with an anomalous plaquette scaling exponent eta(p) = 0.24(1) and an anomalous columnar scaling exponent eta(c) = 0.28(1) at J(2)/J(1) = 0.6. These results are consistent with a potential gapless U(1) spin-liquid phase. However, since the U(1) spin liquid is unstable due to the instanton effect, a valence bond solid order with very small amplitude might develop in the thermodynamic limit. Thus, our numerical results strongly indicate a deconfined quantum critical point at J(2)(c1). Remarkably, all the observed critical exponents are consistent with the J-Q model.}, articleno = {075143}, author = {Wang, Ling and Gu, Zheng-Cheng and Verstraete, Frank and Wen, Xiao-Gang}, issn = {2469-9950}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {7}, pages = {6}, title = {Tensor-product state approach to spin-1/2 square J\unmatched{2081}-J\unmatched{2082} antiferromagnetic Heisenberg model : evidence for deconfined quantum criticality}, url = {http://dx.doi.org/10.1103/PhysRevB.94.075143}, volume = {94}, year = {2016}, }`

- Y. Lee, F. Verstraete, and A. Gendiar, “Boundary-field-driven control of discontinuous phase transitions on hyperbolic lattices,” PHYSICAL REVIEW E, vol. 94, iss. 2, p. 11, 2016.

[Bibtex]`@article{8152461, abstract = {The multistate Potts models on two-dimensional hyperbolic lattices are studied with respect to various boundary effects. The free energy is numerically calculated using the corner transfer matrix renormalization group method. We analyze phase transitions of the Potts models in the thermodynamic limit with respect to contracted boundary layers. A false phase transition is present even if a couple of the boundary layers are contracted. Its significance weakens, as the number of the contracted boundary layers increases, until the correct phase transition (deep inside the bulk) prevails over the false one. For this purpose, we derive a thermodynamic quantity, the so-called bulk excess free energy, which depends on the contracted boundary layers and memorizes additional boundary effects. In particular, the magnetic field is imposed on the outermost boundary layer. While the boundary magnetic field does not affect the second-order phase transition in the bulk if suppressing all the boundary effects on the hyperbolic lattices, the first-order (discontinuous) phase transition is significantly sensitive to the boundary magnetic field. Contrary to the phase transition on the Euclidean lattices, the discontinuous phase transition on the hyperbolic lattices can be continuously controlled (within a certain temperature coexistence region) by varying the boundary magnetic field.}, articleno = {022133}, author = {Lee, Yoju and Verstraete, Frank and Gendiar, Andrej}, issn = {2470-0045}, journal = {PHYSICAL REVIEW E}, language = {eng}, number = {2}, pages = {11}, title = {Boundary-field-driven control of discontinuous phase transitions on hyperbolic lattices}, url = {http://dx.doi.org/10.1103/PhysRevE.94.022133}, volume = {94}, year = {2016}, }`

- L. Vanderstraeten, J. Haegeman, F. Verstraete, and D. Poilblanc, “Quasiparticle interactions in frustrated Heisenberg chains,” PHYSICAL REVIEW B, vol. 93, iss. 23, p. 8, 2016.

[Bibtex]`@article{8152478, abstract = {Interactions between elementary excitations in quasi-one-dimensional antiferromagnets are of experimental relevance and their quantitative theoretical treatment has been a theoretical challenge for many years. Using matrix product states, one can explicitly determine the wave functions of the one-and two-particle excitations, and, consequently, the contributions to dynamical correlations. We apply this framework to the (nonintegrable) frustrated dimerized spin-1/2 chain, a model for generic spin-Peierls systems, where low-energy quasiparticle excitations are bound states of topological solitons. The spin structure factor involving two quasiparticle scattering states is obtained in the thermodynamic limit with full momentum and frequency resolution. This allows very subtle features in the two-particle spectral function to be revealed which, we argue, could be seen, e.g., in inelastic neutron scattering of spin-Peierls compounds under a change of the external pressure.}, articleno = {235108}, author = {Vanderstraeten, Laurens and Haegeman, Jutho and Verstraete, Frank and Poilblanc, Didier}, issn = {2469-9950}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {23}, pages = {8}, title = {Quasiparticle interactions in frustrated Heisenberg chains}, url = {http://dx.doi.org/10.1103/PhysRevB.93.235108}, volume = {93}, year = {2016}, }`

- B. Buyens, F. Verstraete, and K. Van Acoleyen, “Hamiltonian simulation of the Schwinger model at finite temperature,” PHYSICAL REVIEW D, vol. 94, p. 33, 2016.

[Bibtex]`@article{8124552, abstract = {Using Matrix Product Operators (MPO) the Schwinger model is simulated in thermal equilibrium. The variational manifold of gauge invariant MPO is constructed to represent Gibbs states. As a first application the chiral condensate in thermal equilibrium is computed and agreement with earlier studies is found. Furthermore, as a new application the Schwinger model is probed with a fractional charged static quark-antiquark pair separated infinitely far from each other. A critical temperature beyond which the string tension is exponentially suppressed is found, which is in qualitative agreement with analytical studies in the strong coupling limit. Finally, the CT symmetry breaking is investigated and our results strongly suggest that the symmetry is restored at any nonzero temperature.}, articleno = {085018}, author = {Buyens, Boye and Verstraete, Frank and Van Acoleyen, Karel}, issn = {2470-0010}, journal = {PHYSICAL REVIEW D}, language = {eng}, pages = {33}, title = {Hamiltonian simulation of the Schwinger model at finite temperature}, url = {http://dx.doi.org/10.1103/PhysRevD.94.085018}, volume = {94}, year = {2016}, }`

- B. Buyens, J. Haegeman, H. Verschelde, F. Verstraete, and K. Van Acoleyen, “Confinement and string breaking for QED2 in the Hamiltonian picture,” PHYSICAL REVIEW X, vol. 6, iss. 4, p. 32, 2016.

[Bibtex]`@article{8171736, abstract = {The formalism of matrix product states is used to perform a numerical study of (1 + 1)-dimensional QED---also known as the (massive) Schwinger model---in the presence of an external static {\textquotedblleft}quark{\textquotedblright} and {\textquotedblleft}antiquark{\textquotedblright}. We obtain a detailed picture of the transition from the confining state at short interquark distances to the broken-string {\textquotedblleft}hadronized{\textquotedblright} state at large distances, and this for a wide range of couplings, recovering the predicted behavior both in the weak- and strong-coupling limit of the continuum theory. In addition to the relevant local observables like charge and electric field, we compute the (bipartite) entanglement entropy and show that subtraction of its vacuum value results in a UV-finite quantity. We find that both string formation and string breaking leave a clear imprint on the resulting entropy profile. Finally, we also study the case of fractional probe charges, simulating for the first time the phenomenon of partial string breaking.}, articleno = {041040}, author = {Buyens, Boye and Haegeman, Jutho and Verschelde, Henri and Verstraete, Frank and Van Acoleyen, Karel}, issn = {2160-3308}, journal = {PHYSICAL REVIEW X}, language = {eng}, number = {4}, pages = {32}, title = {Confinement and string breaking for QED2 in the Hamiltonian picture}, url = {http://dx.doi.org/10.1103/PhysRevX.6.041040}, volume = {6}, year = {2016}, }`

### 2015

- K. Temme and F. Verstraete, “Quantum chi-squared and goodness of fit testing,” JOURNAL OF MATHEMATICAL PHYSICS, vol. 56, iss. 1, p. 18, 2015.

[Bibtex]`@article{6774590, articleno = {012202}, author = {Temme, Kristan and Verstraete, Frank}, issn = {0022-2488}, journal = {JOURNAL OF MATHEMATICAL PHYSICS}, language = {eng}, number = {1}, pages = {18}, title = {Quantum chi-squared and goodness of fit testing}, url = {http://dx.doi.org/10.1063/1.4905843}, volume = {56}, year = {2015}, }`

- F. Verstraete, Quantum Hamiltonian complexity: worth the wait, 2015.

[Bibtex]`@misc{8024058, author = {Verstraete, Frank}, issn = {1745-2473}, language = {eng}, number = {7}, pages = {524--525}, series = {NATURE PHYSICS}, title = {Quantum Hamiltonian complexity: worth the wait}, url = {http://dx.doi.org/10.1038/nphys3381}, volume = {11}, year = {2015}, }`

- V. Stojevic, J. Haegeman, I. McCulloch, L. Tagliacozzo, and F. Verstraete, “Conformal data from finite entanglement scaling,” PHYSICAL REVIEW B, vol. 91, iss. 3, p. 16, 2015.

[Bibtex]`@article{6774583, abstract = {In this paper, we apply the formalism of translation invariant (continuous) matrix product states in the thermodynamic limit to (1 + 1)-dimensional critical models. Finite bond dimension bounds the entanglement entropy and introduces an effective finite correlation length, so that the state is perturbed away from criticality. The assumption that the scaling hypothesis holds for this kind of perturbation is known in the literature as finite entanglement scaling. We provide further evidence for the validity of finite entanglement scaling and based on this formulate a scaling algorithm to estimate the central charge and critical exponents of the conformally invariant field theories describing the critical models under investigation. The algorithm is applied to three exemplary models; the cMPS version to the nonrelativistic Lieb-Liniger model and the relativistic massless boson, and MPS version to the one-dimensional quantum Ising model at the critical point. Another new aspect to our approach is that we directly use the (c) MPS induced correlation length rather than the bond dimension as scaling parameter. This choice is motivated by several theoretical arguments as well as by the remarkable accuracy of our results.}, articleno = {035120}, author = {Stojevic, Vid and Haegeman, Jutho and McCulloch, IP and Tagliacozzo, Luca and Verstraete, Frank}, issn = {1098-0121}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {3}, pages = {16}, title = {Conformal data from finite entanglement scaling}, url = {http://dx.doi.org/10.1103/PhysRevB.91.035120}, volume = {91}, year = {2015}, }`

- M. Ganahl, M. Aichhorn, H. G. Evertz, P. Thunström, K. Held, and F. Verstraete, “Efficient DMFT impurity solver using real-time dynamics with matrix product states,” PHYSICAL REVIEW B, vol. 92, iss. 15, p. 12, 2015.

[Bibtex]`@article{8024050, abstract = {We propose to calculate spectral functions of quantum impurity models using the time evolving block decimation (TEBD) for matrix product states. The resolution of the spectral function is improved by a so-called linear prediction approach. We apply the method as an impurity solver within the dynamical mean-field theory (DMFT) for the single-and two-band Hubbard model on the Bethe lattice. For the single-band model, we observe sharp features at the inner edges of the Hubbard bands. A finite-size scaling shows that they remain present in the thermodynamic limit. We analyze the real time-dependence of the double occupation after adding a single electron and observe oscillations at the same energy as the sharp feature in the Hubbard band, indicating a long-lived coherent superposition of states that correspond to the Kondo peak and the side peaks. For a two-band Hubbard model, we observe an even richer structure in the Hubbard bands, which cannot be related to a multiplet structure of the impurity, in addition to sharp excitations at the band edges of a type similar to the single-band case.}, articleno = {155132}, author = {Ganahl, Martin and Aichhorn, Markus and Evertz, Hans Gerd and Thunstr{\"o}m, Patrik and Held, Karsten and Verstraete, Frank}, issn = {1098-0121}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {15}, pages = {12}, title = {Efficient DMFT impurity solver using real-time dynamics with matrix product states}, url = {http://dx.doi.org/10.1103/PhysRevB.92.155132}, volume = {92}, year = {2015}, }`

- B. Buyens, J. Haegeman, F. Verstraete, and K. Van Acoleyen, “Tensor networks for gauge field theories,” in PROCEEDINGS OF SCIENCE, 2015, p. 7.

[Bibtex]`@inproceedings{7280916, abstract = {Over the last decade tensor network states (TNS) have emerged as a powerful tool for the study of quantum many body systems. The matrix product states (MPS) are one particular class of TNS and are used for the simulation of (1+1)-dimensional systems. In this proceeding we use MPS to determine the elementary excitations of the Schwinger model in the presence of an electric background field. We obtain an estimate for the value of the background field where the one-particle excitation with the largest energy becomes unstable and decays into two other elementary particles with smaller energy.}, articleno = {280}, author = {Buyens, Boye and Haegeman, Jutho and Verstraete, Frank and Van Acoleyen, Karel}, booktitle = {PROCEEDINGS OF SCIENCE}, issn = {1824-8039}, language = {eng}, location = {Kobe, Japan}, number = {251}, pages = {7}, title = {Tensor networks for gauge field theories}, url = {https://pos.sissa.it/archive/conferences/251/280/LATTICE\%202015\_280.pdf}, year = {2015}, }`

- M. M. Rams, V. Zauner, M. Bal, J. Haegeman, and F. Verstraete, “Truncating an exact matrix product state for the XY model: transfer matrix and its renormalization,” PHYSICAL REVIEW B, vol. 92, iss. 23, p. 13, 2015.

[Bibtex]`@article{7171851, abstract = {We discuss how to analytically obtain an essentially infinite matrix product state (MPS) representation of the ground state of the XY model. On one hand this allows us to illustrate how the Ornstein-Zernike form of the correlation function emerges in the exact case using standard MPS language. On the other hand we study the consequences of truncating the bond dimension of the exact MPS, which is also part of many tensor network algorithms, and analyze how the truncated MPS transfer matrix is representing the dominant part of the exact quantum transfer matrix. In the gapped phase we observe that the correlation length obtained from a truncated MPS approaches the exact value following a power law in effective bond dimension. In the gapless phase we find a good match between a state obtained numerically from standard MPS techniques with finite bond dimension and a state obtained by effective finite imaginary time evolution in our framework. This provides a direct hint for a geometric interpretation of finite entanglement scaling at the critical point in this case. Finally, by analyzing the spectra of transfer matrices, we support the interpretation put forward by V. Zauner et al. [New J. Phys. 17, 053002 (2015)] that the MPS transfer matrix emerges from the quantum transfer matrix though the application of Wilson's numerical renormalization group along the imaginary-time direction.}, articleno = {235150}, author = {Rams, Marek M and Zauner, Valentin and Bal, Matthias and Haegeman, Jutho and Verstraete, Frank}, issn = {1098-0121}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {23}, pages = {13}, title = {Truncating an exact matrix product state for the XY model: transfer matrix and its renormalization}, url = {http://dx.doi.org/10.1103/PhysRevB.92.235150}, volume = {92}, year = {2015}, }`

- L. Vanderstraeten, M. Mariën, F. Verstraete, and J. Haegeman, “Excitations and the tangent space of projected entangled-pair states,” PHYSICAL REVIEW B, vol. 92, iss. 20, p. 5, 2015.

[Bibtex]`@article{7171858, abstract = {We develop tangent space methods for projected entangled-pair states (PEPS) that provide direct access to the low-energy sector of strongly-correlated two-dimensional quantum systems. More specifically, we construct a variational ansatz for elementary excitations on top of PEPS ground states that allows for computing gaps, dispersion relations, and spectral weights directly in the thermodynamic limit. Solving the corresponding variational problem requires the evaluation of momentum transformed two-point and three-point correlation functions on a PEPS background, which we can compute efficiently by using a contraction scheme. As an application we study the spectral properties of the magnons of the Affleck-Kennedy-Lieb-Tasaki model on the square lattice and the anyonic excitations in a perturbed version of Kitaev's toric code.}, articleno = {201111}, author = {Vanderstraeten, Laurens and Mari{\"e}n, Micha{\"e}l and Verstraete, Frank and Haegeman, Jutho}, issn = {1098-0121}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {20}, pages = {5}, title = {Excitations and the tangent space of projected entangled-pair states}, url = {http://dx.doi.org/10.1103/PhysRevB.92.201111}, volume = {92}, year = {2015}, }`

- J. Haegeman, V. Zauner, N. Schuch, and F. Verstraete, “Shadows of anyons and the entanglement structure of topological phases,” NATURE COMMUNICATIONS, vol. 6, p. 8, 2015.

[Bibtex]`@article{7171864, abstract = {The low-temperature dynamics of quantum systems are dominated by the low-energy eigenstates. For two-dimensional systems in particular, exotic phenomena such as topological order and anyon excitations can emerge. While a complete low-energy description of strongly correlated systems is hard to obtain, essential information about the elementary excitations is encoded in the eigenvalue structure of the quantum transfer matrix. Here we study the transfer matrix of topological quantum systems using the tensor network formalism and demonstrate that topological quantum order requires a particular type of 'symmetry breaking' for the fixed point subspace. We also relate physical anyon excitations to domain-wall excitations at the level of the transfer matrix. This formalism enables us to determine the structure of the topological sectors in two-dimensional gapped phases very efficiently, therefore opening novel avenues for studying fundamental questions related to anyon condensation and confinement.}, articleno = {8284}, author = {Haegeman, Jutho and Zauner, V and Schuch, N and Verstraete, Frank}, issn = {2041-1723}, journal = {NATURE COMMUNICATIONS}, language = {eng}, pages = {8}, title = {Shadows of anyons and the entanglement structure of topological phases}, url = {http://dx.doi.org/10.1038/ncomms9284}, volume = {6}, year = {2015}, }`

- J. Haegeman, K. Van Acoleyen, N. Schuch, I. J. Cirac, and F. Verstraete, “Gauging quantum states : from global to local symmetries in many-body systems,” PHYSICAL REVIEW X, vol. 5, iss. 1, p. 10, 2015.

[Bibtex]`@article{6763761, abstract = {We present an operational procedure to transform global symmetries into local symmetries at the level of individual quantum states, as opposed to typical gauging prescriptions for Hamiltonians or Lagrangians. We then construct a compatible gauging map for operators, which preserves locality and reproduces the minimal coupling scheme for simple operators. By combining this construction with the formalism of projected entangled-pair states (PEPS), we can show that an injective PEPS for the matter fields is gauged into a G-injective PEPS for the combined gauge-matter system, which potentially has topological order. We derive the corresponding parent Hamiltonian, which is a frustration-free gauge-theory Hamiltonian closely related to the Kogut-Susskind Hamiltonian at zero coupling constant. We can then introduce gauge dynamics at finite values of the coupling constant by applying a local filtering operation. This scheme results in a low-parameter family of gauge-invariant states of which we can accurately probe the phase diagram, as we illustrate by studying a Z(2) gauge theory with Higgs matter.}, articleno = {011024}, author = {Haegeman, Jutho and Van Acoleyen, Karel and Schuch, Norbert and Cirac, J Ignacio and Verstraete, Frank}, issn = {2160-3308}, journal = {PHYSICAL REVIEW X}, language = {eng}, number = {1}, pages = {10}, title = {Gauging quantum states : from global to local symmetries in many-body systems}, url = {http://dx.doi.org/10.1103/PhysRevX.5.011024}, volume = {5}, year = {2015}, }`

- D. Jennings, C. Brockt, J. Haegeman, T. J. Osborne, and F. Verstraete, “Continuum tensor network field states, path integral representations and spatial symmetries,” NEW JOURNAL OF PHYSICS, vol. 17, p. 22, 2015.

[Bibtex]`@article{7171870, abstract = {A natural way to generalize tensor network variational classes to quantum field systems is via a continuous tensor contraction. This approach is first illustrated for the class of quantum field states known as continuous matrix-product states (cMPS). As a simple example of the path-integral representation we show that the state of a dynamically evolving quantum field admits a natural representation as a cMPS. A completeness argument is also provided that shows that all states in Fock space admit a cMPS representation when the number of variational parameters tends to infinity. Beyond this, we obtain a well-behaved field limit of projected entangled-pair states (PEPS) in two dimensions that provide an abstract class of quantum field states with natural symmetries. We demonstrate how symmetries of the physical field state are encoded within the dynamics of an auxiliary field system of one dimension less. In particular, the imposition of Euclidean symmetries on the physical system requires that the auxiliary system involved in the class' definition must be Lorentz-invariant. The physical field states automatically inherit entropy area laws from the PEPS class, and are fully described by the dissipative dynamics of a lower dimensional virtual field system. Our results lie at the intersection many-body physics, quantum field theory and quantum information theory, and facilitate future exchanges of ideas and insights between these disciplines.}, articleno = {063039}, author = {Jennings, David and Brockt, Christoph and Haegeman, Jutho and Osborne, Tobias J and Verstraete, Frank}, issn = {1367-2630}, journal = {NEW JOURNAL OF PHYSICS}, language = {eng}, pages = {22}, title = {Continuum tensor network field states, path integral representations and spatial symmetries}, url = {http://dx.doi.org/10.1088/1367-2630/17/6/063039}, volume = {17}, year = {2015}, }`

- V. Zauner, D. Draxler, L. Vanderstraeten, M. Degroote, J. Haegeman, M. M. Rams, V. Stojevic, N. Schuch, and F. Verstraete, “Transfer matrices and excitations with matrix product states,” NEW JOURNAL OF PHYSICS, vol. 17, p. 33, 2015.

[Bibtex]`@article{5986701, abstract = {We use the formalism of tensor network states to investigate the relation between static correlation functions in the ground state of local quantum many-body Hamiltonians and the dispersion relations of the corresponding low-energy excitations. In particular, we show that the matrix product state transfer matrix (MPS-TM)---a central object in the computation of static correlation functions---provides important information about the location and magnitude of the minima of the low-energy dispersion relation(s), and we present supporting numerical data for one-dimensional lattice and continuum models as well as two-dimensional lattice models on a cylinder. We elaborate on the peculiar structure of the MPS-TM's eigenspectrum and give several arguments for the close relation between the structure of the low-energy spectrum of the system and the form of the static correlation functions. Finally, we discuss how the MPS-TM connects to the exact quantum transfer matrix of the model at zero temperature. We present a renormalization group argument for obtaining finite bond dimension approximations of the MPS, which allows one to reinterpret variational MPS techniques (such as the density matrix renormalization group) as an application of Wilson's numerical renormalization group along the virtual (imaginary time) dimension of the system.}, articleno = {053002}, author = {Zauner, Valentin and Draxler, Damian and Vanderstraeten, Laurens and Degroote, Matthias and Haegeman, Jutho and Rams, Marek M and Stojevic, Vid and Schuch, Norbert and Verstraete, Frank}, issn = {1367-2630}, journal = {NEW JOURNAL OF PHYSICS}, language = {eng}, pages = {33}, title = {Transfer matrices and excitations with matrix product states}, url = {http://dx.doi.org/10.1088/1367-2630/17/5/053002}, volume = {17}, year = {2015}, }`

- A. Molnar, N. Schuch, F. Verstraete, and I. J. Cirac, “Approximating Gibbs states of local Hamiltonians efficiently with projected entangled pair states,” PHYSICAL REVIEW B, vol. 91, iss. 4, p. 11, 2015.

[Bibtex]`@article{6774576, abstract = {We analyze the error of approximating Gibbs states of local quantum spin Hamiltonians on lattices with projected entangled pair states (PEPS) as a function of the bond dimension (D), temperature (beta(-1)), and system size (N). First, we introduce a compression method in which the bond dimension scales as D = e(O(log22 (N/epsilon))) if beta {\textlangle} O (log(2) N). Second, building on the work of Hastings [M.B. Hastings, Phys. Rev. B 73, 085115 (2006)], we derive a polynomial scaling relation, D = (N/epsilon)(O(beta)). This implies that the manifold of PEPS forms an efficient representation of Gibbs states of local quantum Hamiltonians. From those bounds it also follows that ground states can be approximated with D = N-O(log2 N) whenever the density of states only grows polynomially in the system size. All results hold for any spatial dimension of the lattice.}, articleno = {045138}, author = {Molnar, Andras and Schuch, Norbert and Verstraete, Frank and Cirac, J Ignacio}, issn = {1098-0121}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {4}, pages = {11}, title = {Approximating Gibbs states of local Hamiltonians efficiently with projected entangled pair states}, url = {http://dx.doi.org/10.1103/PhysRevB.91.045138}, volume = {91}, year = {2015}, }`

- S. Barz, B. Dakic, Y. O. Lipp, F. Verstraete, J. Whitfield, and P. Walther, “Linear-optical generation of eigenstates of the two-site XY model,” PHYSICAL REVIEW X, vol. 5, iss. 2, p. 6, 2015.

[Bibtex]`@article{8024159, abstract = {Much of the anticipation accompanying the development of a quantum computer relates to its application to simulating dynamics of another quantum system of interest. Here, we study the building blocks for simulating quantum spin systems with linear optics. We experimentally generate the eigenstates of the XY Hamiltonian under an external magnetic field. The implemented quantum circuit consists of two CNOT gates, which are realized experimentally by harnessing entanglement from a photon source and applying a CPHASE gate. We tune the ratio of coupling constants and the magnetic field by changing local parameters. This implementation of the XY model using linear quantum optics might open the door to future studies of quenching dynamics using linear optics.}, articleno = {021010}, author = {Barz, Stefanie and Dakic, Borivoje and Lipp, Yannick Ole and Verstraete, Frank and Whitfield, James and Walther, Philip}, issn = {2160-3308}, journal = {PHYSICAL REVIEW X}, language = {eng}, number = {2}, pages = {6}, title = {Linear-optical generation of eigenstates of the two-site XY model}, url = {http://dx.doi.org/10.1103/PhysRevX.5.021010}, volume = {5}, year = {2015}, }`

- L. Vanderstraeten, F. Verstraete, and J. Haegeman, “Scattering particles in quantum spin chains,” PHYSICAL REVIEW B, vol. 92, iss. 12, p. 38, 2015.

[Bibtex]`@article{6953753, abstract = {A variational approach for constructing an effective particle description of the low-energy physics of one-dimensional quantum spin chains is presented. Based on the matrix product state formalism, we compute the one- and two-particle excitations as eigenstates of the full microscopic Hamiltonian. We interpret the excitations as particles on a strongly correlated background with nontrivial dispersion relations, spectral weights, and two-particle S matrices. Based on this information, we show how to describe a finite density of excitations as an interacting gas of bosons, using its approximate integrability at low densities. We apply our framework to the Heisenberg antiferromagnetic ladder: we compute the elementary excitation spectrum and the magnon-magnon S matrix, study the formation of bound states, and determine both static and dynamic properties of the magnetized ladder.}, articleno = {125136}, author = {Vanderstraeten, Laurens and Verstraete, Frank and Haegeman, Jutho}, issn = {1098-0121}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {12}, pages = {38}, title = {Scattering particles in quantum spin chains}, url = {http://dx.doi.org/10.1103/PhysRevB.92.125136}, volume = {92}, year = {2015}, }`

- V. Murg, F. Verstraete, R. Schneider, P. Nagy, and O. Legeza, “Tree tensor network state with variable tensor order: an efficient multireference method for strongly correlated systems,” JOURNAL OF CHEMICAL THEORY AND COMPUTATION, vol. 11, iss. 3, pp. 1027-1036, 2015.

[Bibtex]`@article{8196986, abstract = {We study the tree-tensor-network-state (TTNS) method with variable tensor orders for quantum chemistry. TTNS is a variational method to efficiently approximate complete active space (CAS) configuration interaction (CI) wave functions in a tensor product form. TTNS can be considered as a higher order generalization of the matrix product state (MPS) method. The MPS wave function is formulated as products of matrices in a multiparticle basis spanning a truncated Hilbert space of the original CAS-CI problem. These matrices belong to active orbitals organized in a one-dimensional array, while tensors in TTNS are defined upon a tree-like arrangement of the same orbitals. The tree-structure is advantageous since the distance between two arbitrary orbitals in the tree scales only logarithmically with the number of orbitals N, whereas the scaling is linear in the MPS array. It is found to be beneficial from the computational costs point of view to keep strongly correlated orbitals in close vicinity in both arrangements; therefore, the TTNS ansatz is better suited for multireference problems with numerous highly correlated orbitals. To exploit the advantages of TTNS a novel algorithm is designed to optimize the tree tensor network topology based on quantum information theory and entanglement. The superior performance of the TTNS method is illustrated on the ionic-neutral avoided crossing of LiF. It is also shown that the avoided crossing of LiF can be localized using only ground state properties, namely one-orbital entanglement.}, author = {Murg, V and Verstraete, Frank and Schneider, R and Nagy, PR and Legeza, Oe}, issn = {1549-9618}, journal = {JOURNAL OF CHEMICAL THEORY AND COMPUTATION}, language = {eng}, number = {3}, pages = {1027--1036}, title = {Tree tensor network state with variable tensor order: an efficient multireference method for strongly correlated systems}, url = {http://dx.doi.org/10.1021/ct501187j}, volume = {11}, year = {2015}, }`

### 2014

- J. Haegeman, M. Mariën, T. J. Osborne, and F. Verstraete, “Geometry of matrix product states: metric, parallel transport, and curvature,” JOURNAL OF MATHEMATICAL PHYSICS, vol. 55, iss. 2, p. 50, 2014.

[Bibtex]`@article{4404867, articleno = {021902}, author = {Haegeman, Jutho and Mari{\"e}n, Micha{\"e}l and Osborne, Tobias J and Verstraete, Frank}, issn = {0022-2488}, journal = {JOURNAL OF MATHEMATICAL PHYSICS}, language = {eng}, number = {2}, pages = {50}, title = {Geometry of matrix product states: metric, parallel transport, and curvature}, url = {http://dx.doi.org/10.1063/1.4862851}, volume = {55}, year = {2014}, }`

- L. Vanderstraeten, J. Haegeman, T. J. Osborne, and F. Verstraete, “S Matrix from matrix product states,” PHYSICAL REVIEW LETTERS, vol. 112, iss. 25, p. 5, 2014.

[Bibtex]`@article{5837517, abstract = {We use the matrix product state formalism to construct stationary scattering states of elementary excitations in generic one-dimensional quantum lattice systems. Our method is applied to the spin-1 Heisenberg antiferromagnet, for which we calculate the full magnon-magnon S matrix for arbitrary momenta and spin, the two-particle contribution to the spectral function, and higher order corrections to the magnetization curve. As our method provides an accurate microscopic representation of the interaction between elementary excitations, we envisage the description of low-energy dynamics of one-dimensional spin chains in terms of these particlelike excitations.}, articleno = {257202}, author = {Vanderstraeten, Laurens and Haegeman, Jutho and Osborne, Tobias J and Verstraete, Frank}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {25}, pages = {5}, title = {S Matrix from matrix product states}, url = {http://dx.doi.org/10.1103/PhysRevLett.112.257202}, volume = {112}, year = {2014}, }`

- B. Buyens, J. Haegeman, K. Van Acoleyen, H. Verschelde, and F. Verstraete, “Matrix product states for gauge field theories,” PHYSICAL REVIEW LETTERS, vol. 113, iss. 9, 2014.

[Bibtex]`@article{5685200, abstract = {The matrix product state formalism is used to simulate Hamiltonian lattice gauge theories. To this end, we define matrix product state manifolds which are manifestly gauge invariant. As an application, we study (1 + 1)-dimensional one flavor quantum electrodynamics, also known as the massive Schwinger model, and are able to determine very accurately the ground-state properties and elementary one-particle excitations in the continuum limit. In particular, a novel particle excitation in the form of a heavy vector boson is uncovered, compatible with the strong coupling expansion in the continuum. We also study full quantum nonequilibrium dynamics by simulating the real-time evolution of the system induced by a quench in the form of a uniform background electric field.}, articleno = {091601}, author = {Buyens, Boye and Haegeman, Jutho and Van Acoleyen, Karel and Verschelde, Henri and Verstraete, Frank}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {9}, title = {Matrix product states for gauge field theories}, url = {http://dx.doi.org/10.1103/PhysRevLett.113.091601}, volume = {113}, year = {2014}, }`

- R. N. Pfeifer, J. Haegeman, and F. Verstraete, “Faster identification of optimal contraction sequences for tensor networks,” PHYSICAL REVIEW E, vol. 90, iss. 3, p. 18, 2014.

[Bibtex]`@article{5807443, abstract = {The efficient evaluation of tensor expressions involving sums over multiple indices is of significant importance to many fields of research, including quantum many-body physics, loop quantum gravity, and quantum chemistry. The computational cost of evaluating an expression may depend strongly on the order in which the index sums are evaluated, and determination of the operation-minimizing contraction sequence for a single tensor network (single term, in quantum chemistry) is known to be NP-hard. The current preferred solution is an exhaustive search, using either an iterative depth-first approach with pruning or dynamic programming and memoization, but these approaches are impractical for many of the larger tensor network ansatze encountered in quantum many-body physics. We present a modified search algorithm with enhanced pruning which exhibits a performance increase of several orders of magnitude while still guaranteeing identification of an optimal operation-minimizing contraction sequence for a single tensor network.}, articleno = {033315}, author = {Pfeifer, Robert NC and Haegeman, Jutho and Verstraete, Frank}, issn = {1539-3755}, journal = {PHYSICAL REVIEW E}, language = {eng}, number = {3}, pages = {18}, title = {Faster identification of optimal contraction sequences for tensor networks}, url = {http://dx.doi.org/10.1103/PhysRevE.90.033315}, volume = {90}, year = {2014}, }`

- B. Buyens, K. Van Acoleyen, J. Haegeman, and F. Verstraete, “Matrix product states for Hamiltonian lattice gauge theories,” in PROCEEDINGS OF SCIENCE, 2014, p. 7.

[Bibtex]`@inproceedings{5947717, abstract = {Over the last decade tensor network states (TNS) have emerged as a powerful tool for the study of quantum many body systems. The matrix product states (MPS) are one particular case of TNS and are used for the simulation of 1+1 dimensional systems. In [1] we considered the MPS formalism for the simulation of the Hamiltonian lattice gauge formulation of 1+1 dimensional one flavor quantum electrodynamics, also known as the massive Schwinger model. We deduced the ground state and lowest lying excitations. Furthermore, we performed a full quantum real-time simulation for a quench with a uniform background electric field. In this proceeding we continue our work on the Schwinger model. We demonstrate the advantage of working with gauge invariant MPS by comparing with MPS simulations on the full Hilbert space, that includes numerous non-physical gauge variant states. Furthermore, we compute the chiral condensate and recover the predicted UV-divergent behavior.}, articleno = {PoS(Lattice2014)308}, author = {Buyens, Boye and Van Acoleyen, Karel and Haegeman, Jutho and Verstraete, Frank}, booktitle = {PROCEEDINGS OF SCIENCE}, issn = {1824-8039}, language = {eng}, location = {New York, NY, USA}, pages = {7}, title = {Matrix product states for Hamiltonian lattice gauge theories}, url = {http://pos.sissa.it/archive/conferences/214/308/LATTICE2014\_308.pdf}, year = {2014}, }`

- M. Ganahl, P. Thunström, F. Verstraete, K. Held, and H. G. Evertz, “Chebyshev expansion for impurity models using matrix product states,” PHYSICAL REVIEW B, vol. 90, iss. 4, p. 12, 2014.

[Bibtex]`@article{8152484, abstract = {We improve a recently developed expansion technique for calculating real-frequency spectral functions of any one-dimensional model with short-range interactions, by postprocessing computed Chebyshev moments with linear prediction. This can be achieved at virtually no cost, and in sharp contrast to existing methods based on the dampening of the moments, improves the spectral resolution rather than lowering it. We validate the method for the exactly solvable resonating level model and the single impurity Anderson model. It is capable of resolving sharp Kondo resonances, as well as peaks within the Hubbard bands when employed as an impurity solver for dynamical mean-field theory. Our method works at zero temperature and allows for arbitrary discretization of the bath spectrum. It achieves similar precision as the dynamical density matrix renormalization group, at lower cost. We also propose an alternative expansion, of 1 - exp(-tau H) instead of the usual H, which opens the possibility of using established methods for the time evolution of matrix product states to calculate the spectral functions directly.}, articleno = {045144}, author = {Ganahl, Martin and Thunstr{\"o}m, Patrik and Verstraete, Frank and Held, Karsten and Evertz, Hans Gerd}, issn = {1098-0121}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {4}, pages = {12}, title = {Chebyshev expansion for impurity models using matrix product states}, url = {http://dx.doi.org/10.1103/PhysRevB.90.045144}, volume = {90}, year = {2014}, }`

- S. Yang, L. Lehman, D. Poilblanc, K. Van Acoleyen, F. Verstraete, J. Cirac, and N. Schuch, “Edge theories in projected entangled pair state models,” PHYSICAL REVIEW LETTERS, vol. 112, iss. 3, p. 5, 2014.

[Bibtex]`@article{4404873, abstract = {We analyze the low energy excitations of spin lattice systems in two dimensions at zero temperature within the framework of projected entangled pair state models. Perturbations in the bulk give rise to physical excitations located at the edge. We identify the corresponding degrees of freedom, give a procedure to derive the edge Hamiltonian, and illustrate that it can exhibit a rich phase diagram. For topological models, the edge Hamiltonian is constrained by the topological order in the bulk, which gives rise to one-dimensional edge models with unconventional properties; for instance, a topologically ordered bulk can protect a ferromagnetic Ising chain at the edge against spontaneous symmetry breaking.}, articleno = {036402}, author = {Yang, S and Lehman, L and Poilblanc, D and Van Acoleyen, Karel and Verstraete, Frank and Cirac, JI and Schuch, N}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {3}, pages = {5}, title = {Edge theories in projected entangled pair state models}, url = {http://dx.doi.org/10.1103/PhysRevLett.112.036402}, volume = {112}, year = {2014}, }`

### 2013

- J. Haegeman, T. J. Osborne, H. Verschelde, and F. Verstraete, “Entanglement renormalization for quantum fields in real space,” PHYSICAL REVIEW LETTERS, vol. 110, iss. 10, p. 5, 2013.

[Bibtex]`@article{4143156, abstract = {We show how to construct renormalization group (RG) flows of quantum field theories in real space, as opposed to the usual Wilsonian approach in momentum space. This is achieved by generalizing the multiscale entanglement renormalization ansatz to continuum theories. The variational class of wave functions arising from this RG flow are translation invariant and exhibits an an entropy-area law. We illustrate the construction for a free nonrelativistic boson model, and argue that the full power of the construction should emerge in the case of interacting theories.}, articleno = {100402}, author = {Haegeman, Jutho and Osborne, Tobias J and Verschelde, Henri and Verstraete, Frank}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {10}, pages = {5}, title = {Entanglement renormalization for quantum fields in real space}, url = {http://dx.doi.org/10.1103/PhysRevLett.110.100402}, volume = {110}, year = {2013}, }`

- K. Van Acoleyen, M. Mariën, and F. Verstraete, “Entanglement rates and area laws,” PHYSICAL REVIEW LETTERS, vol. 111, iss. 17, p. 5, 2013.

[Bibtex]`@article{4404887, abstract = {We prove an upper bound on the maximal rate at which a Hamiltonian interaction can generate entanglement in a bipartite system. The scaling of this bound as a function of the subsystem dimension on which the Hamiltonian acts nontrivially is optimal and is exponentially improved over previously known bounds. As an application, we show that a gapped quantum many-body spin system on an arbitrary lattice satisfies an area law for the entanglement entropy if and only if any other state with which it is adiabatically connected (i.e., any state in the same phase) also satisfies an area law.}, articleno = {170501}, author = {Van Acoleyen, Karel and Mari{\"e}n, Micha{\"e}l and Verstraete, Frank}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {17}, pages = {5}, title = {Entanglement rates and area laws}, url = {http://dx.doi.org/10.1103/PhysRevLett.111.170501}, volume = {111}, year = {2013}, }`

- J. Haegeman, T. J. Osborne, and F. Verstraete, “Post-matrix product state methods : to tangent space and beyond,” PHYSICAL REVIEW B, vol. 88, iss. 7, p. 35, 2013.

[Bibtex]`@article{4143125, abstract = {We develop in full detail the formalism of tangent states to the manifold of matrix product states, and show how they naturally appear in studying time evolution, excitations, and spectral functions. We focus on the case of systems with translation invariance in the thermodynamic limit, where momentum is a well-defined quantum number. We present some illustrative results and discuss analogous constructions for other variational classes. We also discuss generalizations and extensions beyond the tangent space, and give a general outlook towards post-matrix product methods.}, articleno = {075133}, author = {Haegeman, Jutho and Osborne, Tobias J and Verstraete, Frank}, issn = {1098-0121}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {7}, pages = {35}, title = {Post-matrix product state methods : to tangent space and beyond}, url = {http://dx.doi.org/10.1103/PhysRevB.88.075133}, volume = {88}, year = {2013}, }`

- J. Haegeman, S. Michalakis, B. Nachtergaele, T. J. Osborne, N. Schuch, and F. Verstraete, “Elementary excitations in gapped quantum spin systems,” PHYSICAL REVIEW LETTERS, vol. 111, iss. 8, p. 5, 2013.

[Bibtex]`@article{4143131, articleno = {080401}, author = {Haegeman, Jutho and Michalakis, Spyridon and Nachtergaele, Bruno and Osborne, Tobias J and Schuch, Norbert and Verstraete, Frank}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {8}, pages = {5}, title = {Elementary excitations in gapped quantum spin systems}, url = {http://dx.doi.org/10.1103/PhysRevLett.111.080401}, volume = {111}, year = {2013}, }`

- A. Milsted, J. Haegeman, T. J. Osborne, and F. Verstraete, “Variational matrix product ansatz for nonuniform dynamics in the thermodynamic limit,” PHYSICAL REVIEW B, vol. 88, iss. 15, p. 8, 2013.

[Bibtex]`@article{5639927, abstract = {We describe how to implement the time-dependent variational principle for matrix product states in the thermodynamic limit for nonuniform lattice systems. This is achieved by confining the nonuniformity to a (dynamically growable) finite region with fixed boundary conditions. The suppression of unphysical quasiparticle reflections from the boundary of the nonuniform region is also discussed. Using this algorithm we study the dynamics of localized excitations in infinite systems, which we illustrate in the case of the spin-1 anti-ferromagnetic Heisenberg model and the \unmatched{03d5}4 model.}, articleno = {155116}, author = {Milsted, Ashley and Haegeman, Jutho and Osborne, Tobias J and Verstraete, Frank}, issn = {1098-0121}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {15}, pages = {8}, title = {Variational matrix product ansatz for nonuniform dynamics in the thermodynamic limit}, url = {http://dx.doi.org/10.1103/PhysRevB.88.155116}, volume = {88}, year = {2013}, }`

- J. Haegeman, I. J. Cirac, T. J. Osborne, and F. Verstraete, “Calculus of continuous matrix product states,” PHYSICAL REVIEW B, vol. 88, iss. 8, p. 21, 2013.

[Bibtex]`@article{4143119, abstract = {We discuss various properties of the variational class of continuous matrix product states, a class of Ansatz states for one-dimensional quantum fields that was recently introduced as the direct continuum limit of the highly successful class of matrix product states. We discuss both attributes of the physical states, e.g., by showing in detail how to compute expectation values, as well as properties intrinsic to the representation itself, such as the gauge freedom. We consider general translation noninvariant systems made of several particle species and derive certain regularity properties that need to be satisfied by the variational parameters. We also devote a section to the translation invariant setting in the thermodynamic limit and show how continuous matrix product states possess an intrinsic ultraviolet cutoff. Finally, we introduce a new set of states, which are tangent to the original set of continuous matrix product states. For the case of matrix product states, this construction has recently proven relevant in the development of new algorithms for studying time evolution and elementary excitations of quantum spin chains. We thus lay the foundation for similar developments for one-dimensional quantum fields.}, articleno = {085118}, author = {Haegeman, Jutho and Cirac, J Ignacio and Osborne, Tobias J and Verstraete, Frank}, issn = {1098-0121}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {8}, pages = {21}, title = {Calculus of continuous matrix product states}, url = {http://dx.doi.org/10.1103/PhysRevB.88.085118}, volume = {88}, year = {2013}, }`

- D. Draxler, J. Haegeman, T. J. Osborne, V. Stojevic, L. Vanderstraeten, and F. Verstraete, “Particles, holes, and solitons : a matrix product state approach,” PHYSICAL REVIEW LETTERS, vol. 111, iss. 2, p. 5, 2013.

[Bibtex]`@article{4143148, abstract = {We introduce a variational method for calculating dispersion relations of translation invariant (1 + 1)-dimensional quantum field theories. The method is based on continuous matrix product states and can be implemented efficiently. We study the critical Lieb-Liniger model as a benchmark and excellent agreement with the exact solution is found. Additionally, we observe solitonic signatures of Lieb's type II excitation. In addition, a nonintegrable model is introduced where a U(1)-symmetry breaking term is added to the Lieb-Liniger Hamiltonian. For this model we find evidence of a nontrivial bound-state excitation in the dispersion relation.}, articleno = {020402}, author = {Draxler, Damian and Haegeman, Jutho and Osborne, Tobias J and Stojevic, Vid and Vanderstraeten, Laurens and Verstraete, Frank}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {2}, pages = {5}, title = {Particles, holes, and solitons : a matrix product state approach}, url = {http://dx.doi.org/10.1103/PhysRevLett.111.020402}, volume = {111}, year = {2013}, }`

- L. Wang, D. Poilblanc, Z. Gu, X. Wen, and F. Verstraete, “Constructing a gapless spin-liquid state for the spin-1/2 J\unmatched2081-J\unmatched2082 Heisenberg model on a square lattice,” PHYSICAL REVIEW LETTERS, vol. 111, iss. 3, p. 5, 2013.

[Bibtex]`@article{4143141, abstract = {We construct a class of projected entangled pair states which is exactly the resonating valence bond wave functions endowed with both short range and long range valence bonds. With an energetically preferred resonating valence bond pattern, the wave function is simplified to live in a one-parameter variational space. We tune this variational parameter to minimize the energy for the frustrated spin-1/2 J(1) - J(2) antiferromagnetic Heisenberg model on the square lattice. Taking a cylindrical geometry, we are able to construct four topological sectors with an even or odd number of fluxes penetrating the cylinder and an even or odd number of spinons on the boundary. The energy splitting in different topological sectors is exponentially small with the cylinder perimeter. We find a power law decay of the dimer correlation function on a torus, and a lnL correction to the entanglement entropy, indicating a gapless spin-liquid phase at the optimum parameter.}, articleno = {037202}, author = {Wang, Ling and Poilblanc, Didier and Gu, Zheng-Cheng and Wen, Xiao-Gang and Verstraete, Frank}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {3}, pages = {5}, title = {Constructing a gapless spin-liquid state for the spin-1/2 J\unmatched{2081}-J\unmatched{2082} Heisenberg model on a square lattice}, url = {http://dx.doi.org/10.1103/PhysRevLett.111.037202}, volume = {111}, year = {2013}, }`

- I. Pižorn, F. Verstraete, and R. M. Konik, “Tree tensor networks and entanglement spectra,” PHYSICAL REVIEW B, vol. 88, iss. 19, p. 14, 2013.

[Bibtex]`@article{4404882, abstract = {A tree tensor network variational method is proposed to simulate quantum many-body systems with global symmetries where the optimization is reduced to individual charge configurations. A computational scheme is presented, namely how to extract the entanglement spectra in a bipartite splitting of a loopless tensor network across multiple links of the network, by constructing a matrix product operator for the reduced density operator and simulating its eigenstates. The entanglement spectra of 2 x L, 3 x L, and 4 x L with either open or periodic boundary conditions on the rungs are studied using the presented methods, where it is found that the entanglement spectrum depends not only on the subsystem but also on the boundaries between the subsystems.}, articleno = {195102}, author = {Pi\v{z}orn, Iztok and Verstraete, Frank and Konik, Robert M}, issn = {1098-0121}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {19}, pages = {14}, title = {Tree tensor networks and entanglement spectra}, url = {http://dx.doi.org/10.1103/PhysRevB.88.195102}, volume = {88}, year = {2013}, }`

- M. Schwarz, K. Temme, F. Verstraete, D. Perez-Garcia, and T. S. Cubitt, “Preparing topological projected entangled pair states on a quantum computer,” PHYSICAL REVIEW A, vol. 88, iss. 3, p. 6, 2013.

[Bibtex]`@article{8589169, abstract = {Simulating exotic phases of matter that are not amenable to classical techniques is one of the most important potential applications of quantum information processing. We present an efficient algorithm for preparing a large class of topological quantum states, the G-injective projected entangled pair states (PEPS), on a quantum computer. Important examples include the resonant valence bond states, conjectured to be topological spin liquids. The runtime of the algorithm scales polynomially with the condition number of the PEPS projectors and inverse polynomially in the spectral gap of the PEPS parent Hamiltonian.}, articleno = {032321}, author = {Schwarz, Martin and Temme, Kristan and Verstraete, Frank and Perez-Garcia, David and Cubitt, Toby S}, issn = {1050-2947}, journal = {PHYSICAL REVIEW A}, language = {eng}, number = {3}, pages = {6}, title = {Preparing topological projected entangled pair states on a quantum computer}, url = {http://dx.doi.org/10.1103/PhysRevA.88.032321}, volume = {88}, year = {2013}, }`

### 2012

- V. Murg, V. Korepin, and F. Verstraete, “Algebraic Bethe ansatz and tensor networks,” PHYSICAL REVIEW B, vol. 86, iss. 4, p. 17, 2012.

[Bibtex]`@article{8589191, abstract = {The algebraic Bethe ansatz is a prosperous and well-established method for solving one-dimensional quantum models exactly. The solution of the complex eigenvalue problem is thereby reduced to the solution of a set of algebraic equations. Whereas the spectrum is usually obtained directly, the eigenstates are available only in terms of complex mathematical expressions. This makes it very hard, in general, to extract properties from the states, for example, correlation functions. In our work, we apply the tools of tensor-network states to describe the eigenstates approximately as matrix product states. From the matrix product state expression, we then obtain observables like the structure factor, dimer-dimer correlation functions, chiral correlation functions, and one-particle Green function directly.}, articleno = {045125}, author = {Murg, V and Korepin, VE and Verstraete, Frank}, issn = {2469-9950}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {4}, pages = {17}, title = {Algebraic Bethe ansatz and tensor networks}, url = {http://dx.doi.org/10.1103/PhysRevB.86.045125}, volume = {86}, year = {2012}, }`

- K. Temme, M. M. Wolf, and F. Verstraete, “Stochastic exclusion processes versus coherent transport,” NEW JOURNAL OF PHYSICS, vol. 14, p. 19, 2012.

[Bibtex]`@article{8589164, abstract = {Stochastic exclusion processes play an integral role in the physics of non-equilibrium statistical mechanics. These models are Markovian processes, described by a classical master equation. In this paper, a quantum mechanical version of a stochastic hopping process in one dimension is formulated in terms of a quantum master equation. This allows the investigation of coherent and stochastic evolution in the same formal framework. The focus lies on the non-equilibrium steady state. Two stochastic model systems are considered: the totally asymmetric exclusion process and the fully symmetric exclusion process. The steady-state transport properties of these models are compared to the case with additional coherent evolution, generated by the X X Hamiltonian.}, articleno = {075004}, author = {Temme, Kristan and Wolf, Michael M and Verstraete, Frank}, issn = {1367-2630}, journal = {NEW JOURNAL OF PHYSICS}, language = {eng}, pages = {19}, title = {Stochastic exclusion processes versus coherent transport}, url = {http://dx.doi.org/10.1088/1367-2630/14/7/075004}, volume = {14}, year = {2012}, }`

- K. M. Audenaert, M. Mosonyi, and F. Verstraete, “Quantum state discrimination bounds for finite sample size,” JOURNAL OF MATHEMATICAL PHYSICS, vol. 53, iss. 12, p. 23, 2012.

[Bibtex]`@article{8589166, articleno = {122205}, author = {Audenaert, Koenraad MR and Mosonyi, Milan and Verstraete, Frank}, issn = {0022-2488}, journal = {JOURNAL OF MATHEMATICAL PHYSICS}, language = {eng}, number = {12}, pages = {23}, title = {Quantum state discrimination bounds for finite sample size}, url = {http://dx.doi.org/10.1063/1.4768252}, volume = {53}, year = {2012}, }`

- M. Schwarz, K. Temme, and F. Verstraete, “Preparing projected entangled pair states on a quantum computer,” PHYSICAL REVIEW LETTERS, vol. 108, iss. 11, p. 5, 2012.

[Bibtex]`@article{8589162, abstract = {We present a quantum algorithm to prepare injective projected entangled pair states ( PEPS) on a quantum computer, a class of open tensor networks representing quantum states. The run time of our algorithm scales polynomially with the inverse of the minimum condition number of the PEPS projectors and, essentially, with the inverse of the spectral gap of the PEPS's parent Hamiltonian.}, articleno = {110502}, author = {Schwarz, Martin and Temme, Kristan and Verstraete, Frank}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {11}, pages = {5}, title = {Preparing projected entangled pair states on a quantum computer}, url = {http://dx.doi.org/10.1103/PhysRevLett.108.110502}, volume = {108}, year = {2012}, }`

- B. Pirvu, J. Haegeman, and F. Verstraete, “Matrix product state based algorithm for determining dispersion relations of quantum spin chains with periodic boundary conditions,” PHYSICAL REVIEW B, vol. 85, iss. 3, p. 13, 2012.

[Bibtex]`@article{2119412, abstract = {We study a matrix product state algorithm to approximate excited states of translationally invariant quantum spin systems with periodic boundary conditions. By means of a momentum eigenstate ansatz generalizing the one of Ostlund and Rommer [see S. Ostlund and S. Rommer, Phys. Rev. Lett. 75, 3537 ( 1995); S. Rommer and S. Ostlund, Phys. Rev. B 55, 2164 (1997)], we separate the Hilbert space of the system into subspaces with different momentum. This gives rise to a direct sum of effective Hamiltonians, each one corresponding to a different momentum, and we determine their spectrum by solving a generalized eigenvalue equation. Surprisingly, many branches of the dispersion relation are approximated to a very good precision. We benchmark the accuracy of the algorithm by comparison with the exact solutions and previous numerical results for the quantum Ising, the antiferromagnetic Heisenberg spin-1/2, and the bilinear-biquadratic spin-1 models.}, articleno = {035130}, author = {Pirvu, B and Haegeman, Jutho and Verstraete, Frank}, issn = {1098-0121}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {3}, pages = {13}, title = {Matrix product state based algorithm for determining dispersion relations of quantum spin chains with periodic boundary conditions}, url = {http://dx.doi.org/10.1103/PhysRevB.85.035130}, volume = {85}, year = {2012}, }`

- I. Pizorn and F. Verstraete, “Variational numerical renormalization group : bridging the gap between NRG and density matrix renormalization group,” PHYSICAL REVIEW LETTERS, vol. 108, iss. 6, p. 4, 2012.

[Bibtex]`@article{8589160, abstract = {The numerical renormalization group (NRG) is rephrased as a variational method with the cost function given by the sum of all the energies of the effective low-energy Hamiltonian. This allows us to systematically improve the spectrum obtained by NRG through sweeping. The ensuing algorithm has a lot of similarities to the density matrix renormalization group (DMRG) when targeting many states, and this synergy of NRG and DMRG combines the best of both worlds and extends their applicability. We illustrate this approach with simulations of a quantum spin chain and a single impurity Anderson model where the accuracy of the effective eigenstates is greatly enhanced as compared to the NRG, especially in the transition to the continuum limit.}, articleno = {067202}, author = {Pizorn, Iztok and Verstraete, Frank}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {6}, pages = {4}, title = {Variational numerical renormalization group : bridging the gap between NRG and density matrix renormalization group}, url = {http://dx.doi.org/10.1103/PhysRevLett.108.067202}, volume = {108}, year = {2012}, }`

- J. Wilms, J. Vidal, F. Verstraete, and S. Dusuel, “Finite-temperature mutual information in a simple phase transition,” JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, p. 21, 2012.

[Bibtex]`@article{8589158, abstract = {We study the finite-temperature behavior of the Lipkin-Meshkov-Glick model with a focus on correlation properties as measured by the mutual information. The latter, which quantifies the amount of both classical and quantum correlations, is computed exactly in the two limiting cases of vanishing magnetic field and vanishing temperature. For all other situations, numerical results provide evidence of a finite mutual information at all temperatures except at criticality. There, it diverges as the logarithm of the system size, with a prefactor that can take only two values, depending on whether the critical temperature vanishes or not. Our work provides a simple example in which the mutual information appears as a powerful tool to detect finite-temperature phase transitions, contrary to entanglement measures such as the concurrence.}, articleno = {P01023}, author = {Wilms, Johannes and Vidal, Julien and Verstraete, Frank and Dusuel, Sebastien}, issn = {1742-5468}, journal = {JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT}, language = {eng}, pages = {21}, title = {Finite-temperature mutual information in a simple phase transition}, url = {http://dx.doi.org/10.1088/1742-5468/2012/01/P01023}, year = {2012}, }`

- J. Haegeman, B. Pirvu, D. J. Weir, I. Cirac, T. J. Osborne, H. Verschelde, and F. Verstraete, “Variational matrix product ansatz for dispersion relations,” PHYSICAL REVIEW B, vol. 85, iss. 10, p. 5, 2012.

[Bibtex]`@article{2119320, abstract = {A variational ansatz for momentum eigenstates of translation-invariant quantum spin chains is formulated. The matrix product state ansatz works directly in the thermodynamic limit and allows for an efficient implementation (cubic scaling in the bond dimension) of the variational principle. Unlike previous approaches, the ansatz includes topologically nontrivial states (kinks, domain walls) for systems with symmetry breaking. The method is benchmarked using the spin-1/2 XXZ antiferromagnet and the spin-1 Heisenberg antiferromagnet, and we obtain surprisingly accurate results.}, articleno = {100408}, author = {Haegeman, Jutho and Pirvu, Bogdan and Weir, David J and Cirac, Ignacio and Osborne, Tobias J and Verschelde, Henri and Verstraete, Frank}, issn = {1098-0121}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {10}, pages = {5}, title = {Variational matrix product ansatz for dispersion relations}, url = {http://dx.doi.org/10.1103/PhysRevB.85.100408}, volume = {85}, year = {2012}, }`

- B. Pirvu, G. Vidal, F. Verstraete, and L. Tagliacozzo, “Matrix product states for critical spin chains finite-size versus finite-entanglement scaling,” PHYSICAL REVIEW B, vol. 86, iss. 7, p. 16, 2012.

[Bibtex]`@article{8589189, abstract = {We investigate the use of matrix product states (MPS) to approximate ground states of critical quantum spin chains with periodic boundary conditions (PBC). We identify two regimes in the (N,D) parameter plane, where N is the size of the spin chain and D is the dimension of the MPS matrices. In the first regime, MPS can be used to perform finite size scaling (FSS). In the complementary regime, the MPS simulations show instead the clear signature of finite entanglement scaling (FES). In the thermodynamic limit (or large N limit), only MPS in the FSS regime maintain a finite overlap with the exact ground state. This observation has implications on how to correctly perform FSS with MPS as well as on the performance of recent MPS algorithms for systems with PBC. It also gives clear evidence that critical models can actually be simulated very well with MPS by using the right scaling relations; in the appendixes, we give an alternative derivation of the result of Pollmann et al. [Phys. Rev. Lett. 102, 255701 (2009)] relating the bond dimension of the MPS to an effective correlation length.}, articleno = {075117}, author = {Pirvu, B and Vidal, G and Verstraete, Frank and Tagliacozzo, L}, issn = {1098-0121}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {7}, pages = {16}, title = {Matrix product states for critical spin chains finite-size versus finite-entanglement scaling}, url = {http://dx.doi.org/10.1103/PhysRevB.86.075117}, volume = {86}, year = {2012}, }`

### 2011

- J. Haegeman, I. J. Cirac, T. J. Osborne, I. Pižorn, H. Verschelde, and F. Verstraete, “Time-dependent variational principle for quantum lattices,” PHYSICAL REVIEW LETTERS, vol. 107, iss. 7, p. 5, 2011.

[Bibtex]`@article{2119335, abstract = {We develop a new algorithm based on the time-dependent variational principle applied to matrix product states to efficiently simulate the real-and imaginary-time dynamics for infinite one-dimensional quantum lattices. This procedure (i) is argued to be optimal, (ii) does not rely on the Trotter decomposition and thus has no Trotter error, (iii) preserves all symmetries and conservation laws, and (iv) has low computational complexity. The algorithm is illustrated by using both an imaginary-time and a real-time example.}, articleno = {070601}, author = {Haegeman, Jutho and Cirac, J Ignacio and Osborne, Tobias J and Pi\v{z}orn, Iztok and Verschelde, Henri and Verstraete, Frank}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {7}, pages = {5}, title = {Time-dependent variational principle for quantum lattices}, url = {http://dx.doi.org/10.1103/PhysRevLett.107.070601}, volume = {107}, year = {2011}, }`

- I. Pizorn, L. Wang, and F. Verstraete, “Time evolution of projected entangled pair states in the single-layer picture,” PHYSICAL REVIEW A, vol. 83, iss. 5, p. 6, 2011.

[Bibtex]`@article{8589152, abstract = {We propose an efficient algorithm for simulating quantum many-body systems in two spatial dimensions using projected entangled pair states. This is done by approximating the environment, arising in the context of updating tensors in the process of time evolution, using a single-layered tensor network structure. This significantly reduces the computational costs and allows simulations in a larger submanifold of the Hilbert space as bounded by the bond dimension of the tensor network. We present numerical evidence for stability of the method on an antiferromagnetic isotropic Heisenberg model where good agreement is found with the available accurate results.}, articleno = {052321}, author = {Pizorn, Iztok and Wang, Ling and Verstraete, Frank}, issn = {1050-2947}, journal = {PHYSICAL REVIEW A}, language = {eng}, number = {5}, pages = {6}, title = {Time evolution of projected entangled pair states in the single-layer picture}, url = {http://dx.doi.org/10.1103/PhysRevA.83.052321}, volume = {83}, year = {2011}, }`

- J. Wilms, M. Troyer, and F. Verstraete, “Mutual information in classical spin models,” JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, p. 16, 2011.

[Bibtex]`@article{8589156, abstract = {The total many-body correlations present in finite temperature classical spin systems are studied using the concept of mutual information. As opposed to zero-temperature quantum phase transitions, the total correlations are not maximal at the phase transition, but reach a maximum in the high-temperature paramagnetic phase. The Shannon mutual information and the Renyi mutual information in both Ising and Potts models in two dimensions are calculated numerically by combining matrix product state algorithms and Monte Carlo sampling techniques.}, articleno = {P10011}, author = {Wilms, Johannes and Troyer, Matthias and Verstraete, Frank}, issn = {1742-5468}, journal = {JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT}, language = {eng}, pages = {16}, title = {Mutual information in classical spin models}, url = {http://dx.doi.org/10.1088/1742-5468/2011/10/P10011}, year = {2011}, }`

- D. Poulin, A. Qarry, R. Somma, and F. Verstraete, “Quantum simulation of time-dependent Hamiltonians and the convenient illusion of Hilbert space,” PHYSICAL REVIEW LETTERS, vol. 106, iss. 17, p. 4, 2011.

[Bibtex]`@article{8589150, abstract = {We consider the manifold of all quantum many-body states that can be generated by arbitrary time-dependent local Hamiltonians in a time that scales polynomially in the system size, and show that it occupies an exponentially small volume in Hilbert space. This implies that the overwhelming majority of states in Hilbert space are not physical as they can only be produced after an exponentially long time. We establish this fact by making use of a time-dependent generalization of the Suzuki-Trotter expansion, followed by a well-known counting argument. This also demonstrates that a computational model based on arbitrarily rapidly changing Hamiltonians is no more powerful than the standard quantum circuit model.}, articleno = {170501}, author = {Poulin, David and Qarry, Angie and Somma, Rolando and Verstraete, Frank}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {17}, pages = {4}, title = {Quantum simulation of time-dependent Hamiltonians and the convenient illusion of Hilbert space}, url = {http://dx.doi.org/10.1103/PhysRevLett.106.170501}, volume = {106}, year = {2011}, }`

- I. J. Cirac, D. Poilblanc, N. Schuch, and F. Verstraete, “Entanglement spectrum and boundary theories with projected entangled-pair states,” PHYSICAL REVIEW B, vol. 83, iss. 24, p. 12, 2011.

[Bibtex]`@article{8589154, abstract = {In many physical scenarios, close relations between the bulk properties of quantum systems and theories associated with their boundaries have been observed. In this work, we provide an exact duality mapping between the bulk of a quantum spin system and its boundary using projected entangled-pair states. This duality associates to every region a Hamiltonian on its boundary, in such a way that the entanglement spectrum of the bulk corresponds to the excitation spectrum of the boundary Hamiltonian. We study various specific models: a deformed AKLT model [I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Phys. Rev. Lett. 59, 799 (1987)], an Ising-type model [F. Verstraete, M. M. Wolf, D. Perez-Garcia, and J. I. Cirac, Phys. Rev. Lett. 96, 220601 (2006)], and Kitaev's toric code [A. Kitaev, Ann. Phys. 303, 2 (2003)], both in finite ladders and in infinite square lattices. In the second case, some of those models display quantum phase transitions. We find that a gapped bulk phase with local order corresponds to a boundary Hamiltonian with local interactions, whereas critical behavior in the bulk is reflected on a diverging interaction length of the boundary Hamiltonian. Furthermore, topologically ordered states yield nonlocal Hamiltonians. Because our duality also associates a boundary operator to any operator in the bulk, it in fact provides a full holographic framework for the study of quantum many-body systems via their boundary.}, articleno = {245134}, author = {Cirac, J Ignacio and Poilblanc, Didier and Schuch, Norbert and Verstraete, Frank}, issn = {1098-0121}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {24}, pages = {12}, title = {Entanglement spectrum and boundary theories with projected entangled-pair states}, url = {http://dx.doi.org/10.1103/PhysRevB.83.245134}, volume = {83}, year = {2011}, }`

- K. Temme, T. Osborne, K. Vollbrecht, D. Poulin, and F. Verstraete, “Quantum Metropolis sampling,” NATURE, vol. 471, iss. 7336, pp. 87-90, 2011.

[Bibtex]`@article{8589225, abstract = {The original motivation to build a quantum computer came from Feynman(1), who imagined a machine capable of simulating generic quantum mechanical systems-a task that is believed to be intractable for classical computers. Such a machine could have far-reaching applications in the simulation of many-body quantum physics in condensed-matter, chemical and high-energy systems. Part of Feynman's challenge was met by Lloyd(2), who showed how to approximately decompose the time evolution operator of interacting quantum particles into a short sequence of elementary gates, suitable for operation on a quantum computer. However, this left open the problem of how to simulate the equilibrium and static properties of quantum systems. This requires the preparation of ground and Gibbs states on a quantum computer. For classical systems, this problem is solved by the ubiquitous Metropolis algorithm(3), a method that has basically acquired a monopoly on the simulation of interacting particles. Here we demonstrate how to implement a quantum version of the Metropolis algorithm. This algorithm permits sampling directly from the eigenstates of the Hamiltonian, and thus evades the sign problem present in classical simulations. A small-scale implementation of this algorithm should be achievable with today's technology.}, author = {Temme, K and Osborne, TJ and Vollbrecht, KG and Poulin, D and Verstraete, Frank}, issn = {0028-0836}, journal = {NATURE}, language = {eng}, number = {7336}, pages = {87--90}, title = {Quantum Metropolis sampling}, url = {http://dx.doi.org/10.1038/nature09770}, volume = {471}, year = {2011}, }`

- L. Wang, I. Pizorn, and F. Verstraete, “Monte Carlo simulation with tensor network states,” PHYSICAL REVIEW B, vol. 83, iss. 13, p. 6, 2011.

[Bibtex]`@article{8589148, abstract = {We demonstrate that Monte Carlo sampling can be used to efficiently extract the expectation value of projected entangled pair states with a large virtual bond dimension. We use the simple update rule introduced by H. C. Jiang et al. [Phys. Rev. Lett 101, 090603 (2008)] to obtain the tensors describing the ground state wave function of the antiferromagnetic Heisenberg model and evaluate the finite size energy and staggered magnetization for square lattices with periodic boundary conditions of linear sizes up to L = 16 and virtual bond dimensions up to D = 16. The finite size magnetization errors are 0.003(2) and 0.013(2) at D = 16 for a system of size L = 8,16, respectively. Finite D extrapolation provides exact finite size magnetization for L = 8, and reduces the magnetization error to 0.005(3) for L = 16, significantly improving the previous state-of-the-art results.}, articleno = {134421}, author = {Wang, Ling and Pizorn, Iztok and Verstraete, Frank}, issn = {1098-0121}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {13}, pages = {6}, title = {Monte Carlo simulation with tensor network states}, url = {http://dx.doi.org/10.1103/PhysRevB.83.134421}, volume = {83}, year = {2011}, }`

- B. Pirvu, F. Verstraete, and G. Vidal, “Exploiting translational invariance in matrix product state simulations of spin chains with periodic boundary conditions,” PHYSICAL REVIEW B, vol. 83, iss. 12, p. 14, 2011.

[Bibtex]`@article{8589193, abstract = {We present a matrix product state (MPS) algorithm to approximate ground states of translationally invariant systems with periodic boundary conditions. For a fixed value of the bond dimension D of the MPS, we discuss how to minimize the computational cost to obtain a seemingly optimal MPS approximation to the ground state. In a chain with N sites and correlation length xi, the computational cost formally scales as g(D,xi/N)D-3, where g(D,xi/N) is a nontrivial function. For xi {\textlangle}{\textlangle} N, this scaling reduces to D-3, independent of the system size N, making our method N times faster than previous proposals. We apply the algorithm to obtain MPS approximations for the ground states of the critical quantum Ising and Heisenberg spin-1/2 models as well as for the noncritical Heisenberg spin-1 model. In the critical case, for any chain length N, we find a model-dependent bond dimension D(N) above which the polynomial decay of correlations is faithfully reproduced throughout the entire system.}, articleno = {125104}, author = {Pirvu, B and Verstraete, Frank and Vidal, G}, issn = {2469-9950}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {12}, pages = {14}, title = {Exploiting translational invariance in matrix product state simulations of spin chains with periodic boundary conditions}, url = {http://dx.doi.org/10.1103/PhysRevB.83.125104}, volume = {83}, year = {2011}, }`

### 2010

- K. Temme, M. Kastoryano, M. Ruskai, M. Wolf, and F. Verstraete, “The \ensuremath\chi\texttwosuperior-divergence and mixing times of quantum Markov processes,” JOURNAL OF MATHEMATICAL PHYSICS, vol. 51, iss. 12, p. 19, 2010.

[Bibtex]`@article{8589228, articleno = {122201}, author = {Temme, K and Kastoryano, MJ and Ruskai, MB and Wolf, MM and Verstraete, Frank}, issn = {0022-2488}, journal = {JOURNAL OF MATHEMATICAL PHYSICS}, language = {eng}, number = {12}, pages = {19}, title = {The \ensuremath{\chi}{\texttwosuperior}-divergence and mixing times of quantum Markov processes}, url = {http://dx.doi.org/10.1063/1.3511335}, volume = {51}, year = {2010}, }`

- F. Verstraete and J. Cirac, “Continuous matrix product states for quantum fields,” PHYSICAL REVIEW LETTERS, vol. 104, iss. 19, p. 4, 2010.

[Bibtex]`@article{8589232, abstract = {We define matrix product states in the continuum limit, without any reference to an underlying lattice parameter. This allows us to extend the density matrix renormalization group and variational matrix product state formalism to quantum field theories and continuum models in 1 spatial dimension. We illustrate our procedure with the Lieb-Liniger model.}, articleno = {190405}, author = {Verstraete, Frank and Cirac, JI}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {19}, pages = {4}, title = {Continuous matrix product states for quantum fields}, url = {http://dx.doi.org/10.1103/PhysRevLett.104.190405}, volume = {104}, year = {2010}, }`

- T. J. Osborne, J. Eisert, and F. Verstraete, “Holographic quantum states,” PHYSICAL REVIEW LETTERS, vol. 105, iss. 26, p. 4, 2010.

[Bibtex]`@article{8589146, abstract = {We show how continuous matrix product states of quantum fields can be described in terms of the dissipative nonequilibrium dynamics of a lower-dimensional auxiliary boundary field by demonstrating that the spatial correlation functions of the bulk field correspond to the temporal statistics of the boundary field. This equivalence (1) illustrates an intimate connection between the theory of continuous quantum measurement and quantum field theory, (2) gives an explicit construction of the boundary field allowing the extension of real-space renormalization group methods to arbitrary dimensional quantum field theories without the introduction of a lattice parameter, and (3) yields a novel interpretation of recent cavity QED experiments in terms of quantum field theory, and hence paves the way toward observing genuine quantum phase transitions in such zero-dimensional driven quantum systems.}, articleno = {260401}, author = {Osborne, Tobias J and Eisert, Jens and Verstraete, Frank}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {26}, pages = {4}, title = {Holographic quantum states}, url = {http://dx.doi.org/10.1103/PhysRevLett.105.260401}, volume = {105}, year = {2010}, }`

- B. Pirvu, V. Murg, J. Cirac, and F. Verstraete, “Matrix product operator representations,” NEW JOURNAL OF PHYSICS, vol. 12, p. 13, 2010.

[Bibtex]`@article{8589234, abstract = {We show how to construct relevant families of matrix product operators (MPOs) in one and higher dimensions. These form the building blocks for the numerical simulation methods based on matrix product states and projected entangled pair states. In particular, we construct translationally invariant MPOs suitable for time evolution, and show how such descriptions are possible for Hamiltonians with long-range interactions. We show how these tools can be exploited for constructing new algorithms for simulating quantum spin systems.}, articleno = {025012}, author = {Pirvu, B and Murg, V and Cirac, JI and Verstraete, Frank}, issn = {1367-2630}, journal = {NEW JOURNAL OF PHYSICS}, language = {eng}, pages = {13}, title = {Matrix product operator representations}, url = {http://dx.doi.org/10.1088/1367-2630/12/2/025012}, volume = {12}, year = {2010}, }`

- I. Pizorn and F. Verstraete, “Fermionic implementation of projected entangled pair states algorithm,” PHYSICAL REVIEW B, vol. 81, iss. 24, p. 8, 2010.

[Bibtex]`@article{8589138, abstract = {We present and implement an efficient variational method to simulate two-dimensional finite-size fermionic quantum systems by fermionic projected entangled pair states. The approach differs from the original one due to the fact that there is no need for an extra string bond for contracting the tensor network. The method is tested on a bilinear fermionic model on a square lattice for sizes up to ten by ten where good relative accuracy is achieved. Qualitatively good results are also obtained for an interacting fermionic system.}, articleno = {245110}, author = {Pizorn, Iztok and Verstraete, Frank}, issn = {1098-0121}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {24}, pages = {8}, title = {Fermionic implementation of projected entangled pair states algorithm}, url = {http://dx.doi.org/10.1103/PhysRevB.81.245110}, volume = {81}, year = {2010}, }`

- K. Temme and F. Verstraete, “Stochastic matrix product states,” PHYSICAL REVIEW LETTERS, vol. 104, iss. 21, p. 4, 2010.

[Bibtex]`@article{8589136, abstract = {The concept of stochastic matrix product states is introduced and a natural form for the states is derived. This allows us to define the analogue of Schmidt coefficients for steady states of nonequilibrium stochastic processes. We discuss a new measure for correlations which is analogous to entanglement entropy, the entropy cost S(C), and show that this measure quantifies the bond dimension needed to represent a steady state as a matrix product state. We illustrate these concepts on the basis of the asymmetric exclusion process.}, articleno = {210502}, author = {Temme, Kristan and Verstraete, Frank}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {21}, pages = {4}, title = {Stochastic matrix product states}, url = {http://dx.doi.org/10.1103/PhysRevLett.104.210502}, volume = {104}, year = {2010}, }`

- P. Corboz, G. Evenbly, F. Verstraete, and G. Vidal, “Simulation of interacting fermions with entanglement renormalization,” PHYSICAL REVIEW A, vol. 81, iss. 1, p. 4, 2010.

[Bibtex]`@article{8589131, abstract = {We propose an algorithm to simulate interacting fermions on a two-dimensional lattice. The approach is an extension of the entanglement renormalization technique [Phys. Rev. Lett. 99, 220405 (2007)] and the related multiscale entanglement renormalization ansatz. Benchmark calculations for free and interacting fermions on lattices ranging from 6 x 6 to 162 x 162 sites with periodic boundary conditions confirm the validity of this proposal.}, articleno = {010303}, author = {Corboz, Philippe and Evenbly, Glen and Verstraete, Frank and Vidal, Guifre}, issn = {2469-9926}, journal = {PHYSICAL REVIEW A}, language = {eng}, number = {1}, pages = {4}, title = {Simulation of interacting fermions with entanglement renormalization}, url = {http://dx.doi.org/10.1103/PhysRevA.81.010303}, volume = {81}, year = {2010}, }`

- K. H. Marti, B. Bauer, M. Reiher, M. Troyer, and F. Verstraete, “Complete-graph tensor network states : a new fermionic wave function ansatz for molecules,” NEW JOURNAL OF PHYSICS, vol. 12, p. 16, 2010.

[Bibtex]`@article{8589142, abstract = {We present a class of tensor network states specifically designed to capture the electron correlation within a molecule of arbitrary structure. In this ansatz, the electronic wave function is represented by a complete-graph tensor network (CGTN) ansatz, which implements an efficient reduction of the number of variational parameters by breaking down the complexity of the high-dimensional coefficient tensor of a full-configuration-interaction (FCI) wave function. This ansatz applied to molecules is new and based on a tensor network wave function recently studied in lattice problems. We demonstrate that CGTN states approximate ground states of molecules accurately by comparison of the CGTN and FCI expansion coefficients. The CGTN parametrization is not biased towards any reference configuration, in contrast to many standard quantum chemical methods. This feature allows one to obtain accurate relative energies between CGTN states, which is central to molecular physics and chemistry. We discuss the implications for quantum chemistry and focus on the spin-state problem. Our CGTN approach is applied to the energy splitting of states of different spins for methylene and the strongly correlated ozone molecule at a transition state structure. The parameters of the tensor network ansatz are variationally optimized by means of a parallel-tempering Monte Carlo algorithm.}, articleno = {103008}, author = {Marti, Konrad H and Bauer, Bela and Reiher, Markus and Troyer, Matthias and Verstraete, Frank}, issn = {1367-2630}, journal = {NEW JOURNAL OF PHYSICS}, language = {eng}, pages = {16}, title = {Complete-graph tensor network states : a new fermionic wave function ansatz for molecules}, url = {http://dx.doi.org/10.1088/1367-2630/12/10/103008}, volume = {12}, year = {2010}, }`

- J. Haegeman, I. Cirac, T. J. Osborne, H. Verschelde, and F. Verstraete, “Applying the variational principle to (1+1)-dimensional quantum field theories,” PHYSICAL REVIEW LETTERS, vol. 105, iss. 25, p. 4, 2010.

[Bibtex]`@article{1579094, abstract = {We extend the recently introduced continuous matrix product state variational class to the setting of (1 + 1)-dimensional relativistic quantum field theories. This allows one to overcome the difficulties highlighted by Feynman concerning the application of the variational procedure to relativistic theories, and provides a new way to regularize quantum field theories. A fermionic version of the continuous matrix product state is introduced which is manifestly free of fermion doubling and sign problems. We illustrate the power of the formalism by studying the momentum occupation for free massive Dirac fermions and the chiral symmetry breaking in the Gross-Neveu model.}, articleno = {251601}, author = {Haegeman, Jutho and Cirac, Ignacio and Osborne, Tobias J and Verschelde, Henri and Verstraete, Frank}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {25}, pages = {4}, title = {Applying the variational principle to (1+1)-dimensional quantum field theories}, url = {http://dx.doi.org/10.1103/PhysRevLett.105.251601}, volume = {105}, year = {2010}, }`

- C. V. Kraus, N. Schuch, F. Verstraete, and I. J. Cirac, “Fermionic projected entangled pair states,” PHYSICAL REVIEW A, vol. 81, iss. 5, p. 6, 2010.

[Bibtex]`@article{8589133, abstract = {We introduce a family of states, the fermionic projected entangled pair states (fPEPS), which describe fermionic systems on lattices in arbitrary spatial dimensions. It constitutes the natural extension of another family of states, the PEPS, which efficiently approximate ground and thermal states of spin systems with short-range interactions. We give an explicit mapping between those families, which allows us to extend previous simulation methods to fermionic systems. We also show that fPEPS naturally arise as exact ground states of certain fermionic Hamiltonians. We give an example of such a Hamiltonian, exhibiting criticality while obeying an area law.}, articleno = {052338}, author = {Kraus, Christina V and Schuch, Norbert and Verstraete, Frank and Cirac, J Ignacio}, issn = {1050-2947}, journal = {PHYSICAL REVIEW A}, language = {eng}, number = {5}, pages = {6}, title = {Fermionic projected entangled pair states}, url = {http://dx.doi.org/10.1103/PhysRevA.81.052338}, volume = {81}, year = {2010}, }`

- V. Murg, F. Verstraete, O. Legeza, and R. Noack, “Simulating strongly correlated quantum systems with tree tensor networks,” PHYSICAL REVIEW B, vol. 82, iss. 20, p. 11, 2010.

[Bibtex]`@article{8589230, abstract = {We present a tree-tensor-network-based method to study strongly correlated systems with nonlocal interactions in higher dimensions. Although the momentum-space and quantum-chemistry versions of the density-matrix renormalization group (DMRG) method have long been applied to such systems, the spatial topology of DMRG-based methods allows efficient optimizations to be carried out with respect to one spatial dimension only. Extending the matrix-product-state picture, we formulate a more general approach by allowing the local sites to be coupled to more than two neighboring auxiliary subspaces. Following [Y. Shi, L. Duan, and G. Vidal, Phys. Rev. A 74, 022320 (2006)], we treat a treelike network ansatz with arbitrary coordination number z, where the z=2 case corresponds to the one-dimensional (1D) scheme. For this ansatz, the long-range correlation deviates from the mean-field value polynomially with distance, in contrast to the matrix-product ansatz, which deviates exponentially. The computational cost of the tree-tensor-network method is significantly smaller than that of previous DMRG-based attempts, which renormalize several blocks into a single block. In addition, we investigate the effect of unitary transformations on the local basis states and present a method for optimizing such transformations. For the 1D interacting spinless fermion model, the optimized transformation interpolates smoothly between real space and momentum space. Calculations carried out on small quantum chemical systems support our approach.}, articleno = {205105}, author = {Murg, V and Verstraete, Frank and Legeza, Oe and Noack, RM}, issn = {2469-9950}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {20}, pages = {11}, title = {Simulating strongly correlated quantum systems with tree tensor networks}, url = {http://dx.doi.org/10.1103/PhysRevB.82.205105}, volume = {82}, year = {2010}, }`

### 2009

- N. Schuch and F. Verstraete, “Computational complexity of interacting electrons and fundamental limitations of density functional theory,” NATURE PHYSICS, vol. 5, iss. 10, pp. 732-735, 2009.

[Bibtex]`@article{8588656, abstract = {One of the central problems in quantum mechanics is to determine the ground-state properties of a system of electrons interacting through the Coulomb potential. Since its introduction(1,2), density functional theory has become the most widely used and successful method for simulating systems of interacting electrons. Here, we show that the field of computational complexity imposes fundamental limitations on density functional theory. In particular, if the associated 'universal functional' could be found efficiently, this would imply that any problem in the computational complexity class Quantum Merlin Arthur could be solved efficiently. Quantum Merlin Arthur is the quantum version of the class NP and thus any problem in NP could be solved in polynomial time. This is considered highly unlikely. Our result follows from the fact that finding the ground-state energy of the Hubbard model in an external magnetic field is a hard problem even for a quantum computer, but, given the universal functional, it can be computed efficiently using density functional theory. This work illustrates how the field of quantum computing could be useful even if quantum computers were never built.}, author = {Schuch, Norbert and Verstraete, Frank}, issn = {1745-2473}, journal = {NATURE PHYSICS}, language = {eng}, number = {10}, pages = {732--735}, title = {Computational complexity of interacting electrons and fundamental limitations of density functional theory}, url = {http://dx.doi.org/10.1038/NPHYS1370}, volume = {5}, year = {2009}, }`

- F. Verstraete, I. J. Cirac, and J. I. Latorre, “Quantum circuits for strongly correlated quantum systems,” PHYSICAL REVIEW A, vol. 79, iss. 3, p. 5, 2009.

[Bibtex]`@article{8588651, abstract = {We present an approach to gain detailed control on the quantum simulation of strongly correlated quantum many-body systems by constructing the explicit finite quantum circuits that diagonalize their dynamics. As a particularly simple instance, the full dynamics of a one-dimensional Quantum Ising model in a transverse field with four spins is shown to be reproduced using a quantum circuit of only six local gates. This opens up the possibility of experimentally producing strongly correlated states, their time evolution at zero time, and even thermal superpositions at zero temperature. Our method also allows one to uncover the exact circuits corresponding to models that exhibit topological order and to stabilizer states.}, articleno = {032316}, author = {Verstraete, Frank and Cirac, J Ignacio and Latorre, Jose I}, issn = {2469-9926}, journal = {PHYSICAL REVIEW A}, language = {eng}, number = {3}, pages = {5}, title = {Quantum circuits for strongly correlated quantum systems}, url = {http://dx.doi.org/10.1103/PhysRevA.79.032316}, volume = {79}, year = {2009}, }`

- I. J. Cirac and F. Verstraete, “Renormalization and tensor product states in spin chains and lattices,” JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, vol. 42, iss. 50, p. 34, 2009.

[Bibtex]`@article{8588658, abstract = {We review different descriptions of many-body quantum systems in terms of tensor product states. We introduce several families of such states in terms of the known renormalization procedures, and show that they naturally arise in that context. We concentrate on matrix product states, tree tensor states, multiscale entanglement renormalization ansatz and projected entangled pair states. We highlight some of their properties, and show how they can be used to describe a variety of systems.}, articleno = {504004}, author = {Cirac, J Ignacio and Verstraete, Frank}, issn = {1751-8113}, journal = {JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL}, language = {eng}, number = {50}, pages = {34}, title = {Renormalization and tensor product states in spin chains and lattices}, url = {http://dx.doi.org/10.1088/1751-8113/42/50/504004}, volume = {42}, year = {2009}, }`

- V. Murg, F. Verstraete, and J. Cirac, “Exploring frustrated spin systems using projected entangled pair states,” PHYSICAL REVIEW B, vol. 79, iss. 19, p. 7, 2009.

[Bibtex]`@article{8589243, abstract = {We study the nature of the ground state of the frustrated J(1)-J(2) model and the J(1)-J(3) model using a variational algorithm based on projected entangled pair states. By investigating spin-spin correlation functions, we observe a separation in parameter regions with long- and short-range order. A direct comparison with exact diagonalizations in the subspace of short-range valence bond singlets reveals that the system is well described by states within this subset in the short-range order regions. We discuss the question whether the system forms a spin liquid, a plaquette valence bond crystal, or a columnar dimer crystal in these parameter regions.}, articleno = {195119}, author = {Murg, V and Verstraete, Frank and Cirac, JI}, issn = {2469-9950}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {19}, pages = {7}, title = {Exploring frustrated spin systems using projected entangled pair states}, url = {http://dx.doi.org/10.1103/PhysRevB.79.195119}, volume = {79}, year = {2009}, }`

- F. Verstraete, M. M. Wolf, and I. J. Cirac, “Quantum computation and quantum-state engineering driven by dissipation,” NATURE PHYSICS, vol. 5, iss. 9, pp. 633-636, 2009.

[Bibtex]`@article{8588654, abstract = {The strongest adversary in quantum information science is decoherence, which arises owing to the coupling of a system with its environment(1). The induced dissipation tends to destroy and wash out the interesting quantum effects that give rise to the power of quantum computation(2), cryptography(2) and simulation(3). Whereas such a statement is true for many forms of dissipation, we show here that dissipation can also have exactly the opposite effect: it can be a fully fledged resource for universal quantum computation without any coherent dynamics needed to complement it. The coupling to the environment drives the system to a steady state where the outcome of the computation is encoded. In a similar vein, we show that dissipation can be used to engineer a large variety of strongly correlated states in steady state, including all stabilizer codes, matrix product states(4), and their generalization to higher dimensions(5).}, author = {Verstraete, Frank and Wolf, Michael M and Cirac, J Ignacio}, issn = {1745-2473}, journal = {NATURE PHYSICS}, language = {eng}, number = {9}, pages = {633--636}, title = {Quantum computation and quantum-state engineering driven by dissipation}, url = {http://dx.doi.org/10.1038/NPHYS1342}, volume = {5}, year = {2009}, }`

- M. Banuls, M. Hastings, F. Verstraete, and J. Cirac, “Matrix product states for dynamical simulation of infinite chains,” PHYSICAL REVIEW LETTERS, vol. 102, iss. 24, p. 4, 2009.

[Bibtex]`@article{8589241, abstract = {We propose a new method for computing the ground state properties and the time evolution of infinite chains based on a transverse contraction of the tensor network. The method does not require finite size extrapolation and avoids explicit truncation of the bond dimension along the evolution. By folding the network in the time direction prior to contraction, time-dependent expectation values and dynamic correlation functions can be computed after much longer evolution time than with any previous method. Moreover, the algorithm we propose can be used for the study of some noninvariant infinite chains, including impurity models.}, articleno = {240603}, author = {Banuls, MC and Hastings, MB and Verstraete, Frank and Cirac, JI}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {24}, pages = {4}, title = {Matrix product states for dynamical simulation of infinite chains}, url = {http://dx.doi.org/10.1103/PhysRevLett.102.240603}, volume = {102}, year = {2009}, }`

- A. Weichselbaum, F. Verstraete, U. Schollwoeck, J. Cirac, and J. von Delft, “Variational matrix-product-state approach to quantum impurity models,” PHYSICAL REVIEW B, vol. 80, iss. 16, p. 7, 2009.

[Bibtex]`@article{8589237, abstract = {We present a unified framework for renormalization group methods, including Wilson's numerical renormalization group (NRG), and White's density-matrix renormalization group (DMRG), within the language of matrix-product-states. This allows improvements over Wilson's NRG for quantum impurity models, as we illustrate for the one-channel Kondo model. Moreover, we use a variational method for evaluating Green's functions. The proposed method is more flexible in its description of spectral properties at finite frequencies, opening the way to time-dependent, out-of-equilibrium impurity problems. It also substantially improves computational efficiency for one-channel impurity problems, suggesting potentially linear scaling of complexity for n-channel problems.}, articleno = {165117}, author = {Weichselbaum, A and Verstraete, Frank and Schollwoeck, U and Cirac, JI and von Delft, Jan}, issn = {1098-0121}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {16}, pages = {7}, title = {Variational matrix-product-state approach to quantum impurity models}, url = {http://dx.doi.org/10.1103/PhysRevB.80.165117}, volume = {80}, year = {2009}, }`

- R. Huebener, C. Kruszynska, L. Hartmann, W. Duer, F. Verstraete, J. Eisert, and M. Plenio, “Renormalization algorithm with graph enhancement,” PHYSICAL REVIEW A, vol. 79, iss. 2, p. 6, 2009.

[Bibtex]`@article{8589248, abstract = {We introduce a class of variational states to describe quantum many-body systems. This class generalizes matrix product states which underlie the density-matrix renormalization-group approach by combining them with weighted graph states. States within this class may (i) possess arbitrarily long-ranged two-point correlations, (ii) exhibit an arbitrary degree of block entanglement entropy up to a volume law, (iii) be taken translationally invariant, while at the same time (iv) local properties and two-point correlations can be computed efficiently. This variational class of states can be thought of as being prepared from matrix product states, followed by commuting unitaries on arbitrary constituents, hence truly generalizing both matrix product and weighted graph states. We use this class of states to formulate a renormalization algorithm with graph enhancement and present numerical examples, demonstrating that improvements over density-matrix renormalization-group simulations can be achieved in the simulation of ground states and quantum algorithms. Further generalizations, e.g., to higher spatial dimensions, are outlined.}, articleno = {022317}, author = {Huebener, R and Kruszynska, C and Hartmann, L and Duer, W and Verstraete, Frank and Eisert, J and Plenio, MB}, issn = {1050-2947}, journal = {PHYSICAL REVIEW A}, language = {eng}, number = {2}, pages = {6}, title = {Renormalization algorithm with graph enhancement}, url = {http://dx.doi.org/10.1103/PhysRevA.79.022317}, volume = {79}, year = {2009}, }`

### 2008

- F. Verstraete, V. Murg, and J. Cirac, “Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems,” ADVANCES IN PHYSICS, vol. 57, iss. 2, pp. 143-224, 2008.

[Bibtex]`@article{8589270, abstract = {This article reviews recent developments in the theoretical understanding and the numerical implementation of variational renormalization group methods using matrix product states and projected entangled pair states.}, author = {Verstraete, Frank and Murg, V and Cirac, JI}, issn = {0001-8732}, journal = {ADVANCES IN PHYSICS}, language = {eng}, number = {2}, pages = {143--224}, title = {Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems}, url = {http://dx.doi.org/10.1080/14789940801912366}, volume = {57}, year = {2008}, }`

- N. Schuch, I. Cirac, and F. Verstraete, “Computational difficulty of finding matrix product ground states,” PHYSICAL REVIEW LETTERS, vol. 100, iss. 25, p. 4, 2008.

[Bibtex]`@article{8588649, abstract = {We determine the computational difficulty of finding ground states of one-dimensional (1D) Hamiltonians, which are known to be matrix product states (MPS). To this end, we construct a class of 1D frustration-free Hamiltonians with unique MPS ground states and a polynomial gap above, for which finding the ground state is at least as hard as factoring. Without the uniqueness of the ground state, the problem becomes NP complete, and thus for these Hamiltonians it cannot even be certified that the ground state has been found. This poses new bounds on convergence proofs for variational methods that use MPS.}, articleno = {250501}, author = {Schuch, Norbert and Cirac, Ignacio and Verstraete, Frank}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {25}, pages = {4}, title = {Computational difficulty of finding matrix product ground states}, url = {http://dx.doi.org/10.1103/PhysRevLett.100.250501}, volume = {100}, year = {2008}, }`

- N. Schuch, M. M. Wolf, F. Verstraete, and I. J. Cirac, “Simulation of quantum many-body systems with strings of operators and Monte Carlo tensor contractions,” PHYSICAL REVIEW LETTERS, vol. 100, iss. 4, p. 4, 2008.

[Bibtex]`@article{8588645, abstract = {We introduce string-bond states, a class of states obtained by placing strings of operators on a lattice, which encompasses the relevant states in quantum information. For string-bond states, expectation values of local observables can be computed efficiently using Monte Carlo sampling, making them suitable for a variational algorithm which extends the density matrix renormalization group to higher dimensional and irregular systems. Numerical results demonstrate the applicability of these states to the simulation of many-body systems.}, articleno = {040501}, author = {Schuch, Norbert and Wolf, Michael M and Verstraete, Frank and Cirac, J Ignacio}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {4}, pages = {4}, title = {Simulation of quantum many-body systems with strings of operators and Monte Carlo tensor contractions}, url = {http://dx.doi.org/10.1103/PhysRevLett.100.040501}, volume = {100}, year = {2008}, }`

- K. Audenaert, M. Nussbaum, A. Szkola, and F. Verstraete, “Asymptotic error rates in quantum hypothesis testing,” COMMUNICATIONS IN MATHEMATICAL PHYSICS, vol. 279, iss. 1, pp. 251-283, 2008.

[Bibtex]`@article{8589268, abstract = {We consider the problem of discriminating between two different states of a finite quantum system in the setting of large numbers of copies, and find a closed form expression for the asymptotic exponential rate at which the error probability tends to zero. This leads to the identification of the quantum generalisation of the classical Chernoff distance, which is the corresponding quantity in classical symmetric hypothesis testing. The proof relies on two new techniques introduced by the authors, which are also well suited to tackle the corresponding problem in asymmetric hypothesis testing, yielding the quantum generalisation of the classical Hoeffding bound. This has been done by Hayashi and Nagaoka for the special case where the states have full support. The goal of this paper is to present the proofs of these results in a unified way and in full generality, allowing hypothesis states with different supports. From the quantum Hoeffding bound, we then easily derive quantum Stein's Lemma and quantum Sanov's theorem. We give an in-depth treatment of the properties of the quantum Chernoff distance, and argue that it is a natural distance measure on the set of density operators, with a clear operational meaning.}, author = {Audenaert, KMR and Nussbaum, M and Szkola, A and Verstraete, Frank}, issn = {0010-3616}, journal = {COMMUNICATIONS IN MATHEMATICAL PHYSICS}, language = {eng}, number = {1}, pages = {251--283}, title = {Asymptotic error rates in quantum hypothesis testing}, url = {http://dx.doi.org/10.1007/s00220-008-0417-5}, volume = {279}, year = {2008}, }`

- N. Schuch, M. M. Wolf, F. Verstraete, and I. J. Cirac, “Entropy scaling and simulability by matrix product states,” PHYSICAL REVIEW LETTERS, vol. 100, iss. 3, p. 4, 2008.

[Bibtex]`@article{8588643, abstract = {We investigate the relation between the scaling of block entropies and the efficient simulability by matrix product states (MPSs) and clarify the connection both for von Neumann and Renyi entropies. Most notably, even states obeying a strict area law for the von Neumann entropy are not necessarily approximable by MPSs. We apply these results to illustrate that quantum computers might outperform classical computers in simulating the time evolution of quantum systems, even for completely translational invariant systems subject to a time-independent Hamiltonian.}, articleno = {030504}, author = {Schuch, Norbert and Wolf, Michael M and Verstraete, Frank and Cirac, J Ignacio}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {3}, pages = {4}, title = {Entropy scaling and simulability by matrix product states}, url = {http://dx.doi.org/10.1103/PhysRevLett.100.030504}, volume = {100}, year = {2008}, }`

- D. Perez-Garcia, M. Wolf, M. Sanz, F. Verstraete, and J. Cirac, “String order and symmetries in quantum spin lattices,” PHYSICAL REVIEW LETTERS, vol. 100, iss. 16, p. 4, 2008.

[Bibtex]`@article{8589266, abstract = {We show that the existence of string order in a given quantum state is intimately related to the presence of a local symmetry by proving that both concepts are equivalent within the framework of finitely correlated states. Once this connection is established, we provide a complete characterization of local symmetries in these states. The results allow us to understand in a straightforward way many of the properties of string order parameters, like their robustness or fragility under perturbations and their typical disappearance beyond strictly one-dimensional lattices. We propose and discuss an alternative definition, ideally suited for detecting phase transitions, and generalizations to two and more spatial dimensions.}, articleno = {167202}, author = {Perez-Garcia, D and Wolf, MM and Sanz, M and Verstraete, Frank and Cirac, JI}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {16}, pages = {4}, title = {String order and symmetries in quantum spin lattices}, url = {http://dx.doi.org/10.1103/PhysRevLett.100.167202}, volume = {100}, year = {2008}, }`

- J. Jordan, R. Orus, G. Vidal, F. Verstraete, and J. Cirac, “Classical simulation of infinite-size quantum lattice systems in two spatial dimensions,” PHYSICAL REVIEW LETTERS, vol. 101, iss. 25, p. 4, 2008.

[Bibtex]`@article{8589254, abstract = {We present an algorithm to simulate two-dimensional quantum lattice systems in the thermodynamic limit. Our approach builds on the projected entangled-pair state algorithm for finite lattice systems [F. Verstraete and J. I. Cirac, arxiv: cond-mat/0407066] and the infinite time-evolving block decimation algorithm for infinite one-dimensional lattice systems [G. Vidal, Phys. Rev. Lett. 98, 070201 (2007)]. The present algorithm allows for the computation of the ground state and the simulation of time evolution in infinite two-dimensional systems that are invariant under translations. We demonstrate its performance by obtaining the ground state of the quantum Ising model and analyzing its second order quantum phase transition.}, articleno = {250602}, author = {Jordan, J and Orus, R and Vidal, G and Verstraete, Frank and Cirac, JI}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {25}, pages = {4}, title = {Classical simulation of infinite-size quantum lattice systems in two spatial dimensions}, url = {http://dx.doi.org/10.1103/PhysRevLett.101.250602}, volume = {101}, year = {2008}, }`

- D. Perez-Garcia, F. Verstraete, M. Wolf, and J. Cirac, “PEPS as unique ground states of local Hamiltonians,” QUANTUM INFORMATION & COMPUTATION, vol. 8, iss. 6-7, pp. 650-663, 2008.

[Bibtex]`@article{8589260, abstract = {In this paper we consider projected entangled pair states (PEPS) on arbitrary lattices. We construct local parent Hamiltonians for each PEPS and isolate a condition under which the state is the unique ground state of the Hamiltonian. This condition, verified by generic PEPS and examples like the AKLT model, is an injective relation between the boundary and the bulk of any local region. While it implies the existence of an energy gap in the 1D case we will show that in certain cases (e.g., on a 2D hexagonal lattice) the parent Hamiltonian can be gapless with a critical ground state. To show this we invoke a mapping between classical and quantum models and prove that in these cases the injectivity relation between boundary and bulk solely depends on the lattice geometry.}, author = {Perez-Garcia, D and Verstraete, Frank and Wolf, MM and Cirac, JI}, issn = {1533-7146}, journal = {QUANTUM INFORMATION \& COMPUTATION}, language = {eng}, number = {6-7}, pages = {650--663}, title = {PEPS as unique ground states of local Hamiltonians}, volume = {8}, year = {2008}, }`

- M. M. Wolf, F. Verstraete, M. B. Hastings, and I. J. Cirac, “Area laws in quantum systems : mutual information and correlations,” PHYSICAL REVIEW LETTERS, vol. 100, iss. 7, p. 4, 2008.

[Bibtex]`@article{8588647, abstract = {The holographic principle states that on a fundamental level the information content of a region should depend on its surface area rather than on its volume. In this Letter we show that this phenomenon not only emerges in the search for new Planck-scale laws but also in lattice models of classical and quantum physics: the information contained in part of a system in thermal equilibrium obeys an area law. While the maximal information per unit area depends classically only on the number of degrees of freedom, it may diverge as the inverse temperature in quantum systems. It is shown that an area law is generally implied by a finite correlation length when measured in terms of the mutual information.}, articleno = {070502}, author = {Wolf, Michael M and Verstraete, Frank and Hastings, Matthew B and Cirac, J Ignacio}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {7}, pages = {4}, title = {Area laws in quantum systems : mutual information and correlations}, url = {http://dx.doi.org/10.1103/PhysRevLett.100.070502}, volume = {100}, year = {2008}, }`

- M. Banuls, D. Perez-Garcia, M. Wolf, F. Verstraete, and J. Cirac, “Sequentially generated states for the study of two-dimensional systems,” PHYSICAL REVIEW A, vol. 77, iss. 5, p. 9, 2008.

[Bibtex]`@article{8589264, abstract = {Matrix product states can be defined as the family of quantum states that can be sequentially generated in a one-dimensional system [Schon et al., Phys. Rev. Lett. 95, 110503 (2005)]. We introduce a family of states that extends this definition to two dimensions. Like in matrix product states, expectation values of few body observables can be efficiently evaluated and, for the case of translationally invariant systems, the correlation functions decay exponentially with the distance. We show that such states are a subclass of projected entangled pair states and investigate their suitability for approximating the ground states of local Hamiltonians.}, articleno = {052306}, author = {Banuls, MC and Perez-Garcia, D and Wolf, MM and Verstraete, Frank and Cirac, JI}, issn = {1050-2947}, journal = {PHYSICAL REVIEW A}, language = {eng}, number = {5}, pages = {9}, title = {Sequentially generated states for the study of two-dimensional systems}, url = {http://dx.doi.org/10.1103/PhysRevA.77.052306}, volume = {77}, year = {2008}, }`

- M. Aguado, G. Brennen, F. Verstraete, and J. Cirac, “Creation, manipulation, and detection of Abelian and non-Abelian Anyons in optical lattices,” PHYSICAL REVIEW LETTERS, vol. 101, iss. 26, p. 4, 2008.

[Bibtex]`@article{8589252, abstract = {Anyons are particlelike excitations of strongly correlated phases of matter with fractional statistics, characterized by nontrivial changes in the wave function, generalizing Bose and Fermi statistics, when two of them are interchanged. This can be used to perform quantum computations [A. Yu. Kitaev, Ann. Phys. (N.Y.) 303, 2 (2003)]. We show how to simulate the creation and manipulation of Abelian and non-Abelian anyons in topological lattice models using trapped atoms in optical lattices. Our proposal, feasible with present technology, requires an ancilla particle which can undergo single-particle gates, be moved close to each constituent of the lattice and undergo a simple quantum gate, and be detected.}, articleno = {260501}, author = {Aguado, M and Brennen, GK and Verstraete, Frank and Cirac, JI}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {26}, pages = {4}, title = {Creation, manipulation, and detection of Abelian and non-Abelian Anyons in optical lattices}, url = {http://dx.doi.org/10.1103/PhysRevLett.101.260501}, volume = {101}, year = {2008}, }`

- S. Perseguers, L. Jiang, N. Schuch, F. Verstraete, M. Lukin, J. Cirac, and K. Vollbrecht, “One-shot entanglement generation over long distances in noisy quantum networks,” PHYSICAL REVIEW A, vol. 78, iss. 6, p. 6, 2008.

[Bibtex]`@article{8589257, abstract = {We consider the problem of creating a long-distance entangled state between two stations of a network, where neighboring nodes are connected by noisy quantum channels. We show that any two stations can share an entangled pair if the effective probability for the quantum errors is below a certain threshold, which is achieved by a local encoding of the qubits and a global bit-flip correction. In contrast to the conventional quantum-repeater schemes, we do not need to store the qubits in quantum memory for a long time: our protocol is a one-shot process (i.e., the elementary entangled pairs are used only once) involving one-way classical communication. Furthermore, the overhead of local resources increases only logarithmically with the size of the network, making our proposal favorable to long-distance quantum communication.}, articleno = {062324}, author = {Perseguers, S and Jiang, L and Schuch, N and Verstraete, Frank and Lukin, MD and Cirac, JI and Vollbrecht, KGH}, issn = {2469-9926}, journal = {PHYSICAL REVIEW A}, language = {eng}, number = {6}, pages = {6}, title = {One-shot entanglement generation over long distances in noisy quantum networks}, url = {http://dx.doi.org/10.1103/PhysRevA.78.062324}, volume = {78}, year = {2008}, }`

### 2007

- K. Audenaert, J. Calsamiglia, R. Munoz-Tapia, E. Bagan, L. Masanes, A. Acin, and F. Verstraete, “Discriminating states : the quantum Chernoff bound,” PHYSICAL REVIEW LETTERS, vol. 98, iss. 16, p. 4, 2007.

[Bibtex]`@article{8589274, abstract = {We consider the problem of discriminating two different quantum states in the setting of asymptotically many copies, and determine the minimal probability of error. This leads to the identification of the quantum Chernoff bound, thereby solving a long-standing open problem. The bound reduces to the classical Chernoff bound when the quantum states under consideration commute. The quantum Chernoff bound is the natural symmetric distance measure between quantum states because of its clear operational meaning and because it does not seem to share some of the undesirable features of other distance measures.}, articleno = {160501}, author = {Audenaert, KMR and Calsamiglia, J and Munoz-Tapia, R and Bagan, E and Masanes, Ll and Acin, A and Verstraete, Frank}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {16}, pages = {4}, title = {Discriminating states : the quantum Chernoff bound}, url = {http://dx.doi.org/10.1103/PhysRevLett.98.160501}, volume = {98}, year = {2007}, }`

- Y. Liu, M. Christandl, and F. Verstraete, “Quantum computational complexity of the N-representability problem : QMA complete,” PHYSICAL REVIEW LETTERS, vol. 98, iss. 11, p. 4, 2007.

[Bibtex]`@article{8590932, abstract = {We study the computational complexity of the N-representability problem in quantum chemistry. We show that this problem is quantum Merlin-Arthur complete, which is the quantum generalization of nondeterministic polynomial time complete. Our proof uses a simple mapping from spin systems to fermionic systems, as well as a convex optimization technique that reduces the problem of finding ground states to N representability.}, articleno = {110503}, author = {Liu, Yi-Kai and Christandl, Matthias and Verstraete, Frank}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {11}, pages = {4}, title = {Quantum computational complexity of the N-representability problem : QMA complete}, url = {http://dx.doi.org/10.1103/PhysRevLett.98.110503}, volume = {98}, year = {2007}, }`

- V. Murg, F. Verstraete, and J. Cirac, “Variational study of hard-core bosons in a two-dimensional optical lattice using projected entangled pair states,” PHYSICAL REVIEW A, vol. 75, iss. 3, p. 8, 2007.

[Bibtex]`@article{8590935, abstract = {We have studied the system of hard-core bosons on a two-dimensional optical lattice using a variational algorithm based on projected entangled-pair states. We have investigated the ground-state properties of the system as well as the responses of the system to sudden changes in the parameters. We have compared our results to mean-field results based on a Gutzwiller ansatz.}, articleno = {033605}, author = {Murg, V and Verstraete, Frank and Cirac, JI}, issn = {1050-2947}, journal = {PHYSICAL REVIEW A}, language = {eng}, number = {3}, pages = {8}, title = {Variational study of hard-core bosons in a two-dimensional optical lattice using projected entangled pair states}, url = {http://dx.doi.org/10.1103/PhysRevA.75.033605}, volume = {75}, year = {2007}, }`

- D. Perez-Garcia, F. Verstraete, M. Wolf, and J. Cirac, “Matrix product state representations,” QUANTUM INFORMATION & COMPUTATION, vol. 7, iss. 5-6, pp. 401-430, 2007.

[Bibtex]`@article{8589272, abstract = {This work gives a detailed investigation of matrix product state (TOPS) representations for pure multipartite quantum states. We determine the freedom in representations with and without translation symmetry, derive respective canonical forms and provide efficient methods for obtaining them. Results on frustration free Hamiltonians and the generation of MPS are extended, and the use of the MPS-representation for classical simulations of quantum systems is discussed.}, author = {Perez-Garcia, D and Verstraete, Frank and Wolf, MM and Cirac, JI}, issn = {1533-7146}, journal = {QUANTUM INFORMATION \& COMPUTATION}, language = {eng}, number = {5-6}, pages = {401--430}, title = {Matrix product state representations}, volume = {7}, year = {2007}, }`

- N. Schuch, M. M. Wolf, F. Verstraete, and I. J. Cirac, “Computational complexity of projected entangled pair states,” PHYSICAL REVIEW LETTERS, vol. 98, iss. 14, p. 4, 2007.

[Bibtex]`@article{8588641, abstract = {We determine the computational power of preparing projected entangled pair states (PEPS), as well as the complexity of classically simulating them, and generally the complexity of contracting tensor networks. While creating PEPS allows us to solve PP problems, the latter two tasks are both proven to be \#P-complete. We further show how PEPS can be used to approximate ground states of gapped Hamiltonians and that creating them is easier than creating arbitrary PEPS. The main tool for our proofs is a duality between PEPS and postselection which allows us to use existing results from quantum complexity.}, articleno = {140506}, author = {Schuch, Norbert and Wolf, Michael M and Verstraete, Frank and Cirac, J Ignacio}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {14}, pages = {4}, title = {Computational complexity of projected entangled pair states}, url = {http://dx.doi.org/10.1103/PhysRevLett.98.140506}, volume = {98}, year = {2007}, }`

### 2006

- F. Verstraete and J. Cirac, “Matrix product states represent ground states faithfully,” PHYSICAL REVIEW B, vol. 73, iss. 9, p. 8, 2006.

[Bibtex]`@article{8590968, abstract = {We quantify how well matrix product states approximate exact ground states of one-dimensional quantum spin systems as a function of the number of spins and the entropy of blocks of spins. We also investigate the convex set of local reduced density operators of translational invariant systems. The results give a theoretical justification for the high accuracy of renormalization group algorithms and justifies their use even in the case of critical systems.}, articleno = {094423}, author = {Verstraete, Frank and Cirac, JI}, issn = {2469-9950}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {9}, pages = {8}, title = {Matrix product states represent ground states faithfully}, url = {http://dx.doi.org/10.1103/PhysRevB.73.094423}, volume = {73}, year = {2006}, }`

- T. J. Osborne and F. Verstraete, “General monogamy inequality for bipartite qubit entanglement,” PHYSICAL REVIEW LETTERS, vol. 96, iss. 22, p. 4, 2006.

[Bibtex]`@article{8588637, abstract = {We consider multipartite states of qubits and prove that their bipartite quantum entanglement, as quantified by the concurrence, satisfies a monogamy inequality conjectured by Coffman, Kundu, and Wootters. We relate this monogamy inequality to the concept of frustration of correlations in quantum spin systems.}, articleno = {220503}, author = {Osborne, Tobias J and Verstraete, Frank}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {22}, pages = {4}, title = {General monogamy inequality for bipartite qubit entanglement}, url = {http://dx.doi.org/10.1103/PhysRevLett.96.220503}, volume = {96}, year = {2006}, }`

- S. Bravyi, M. Hastings, and F. Verstraete, “Lieb-Robinson bounds and the generation of correlations and topological quantum order,” PHYSICAL REVIEW LETTERS, vol. 97, iss. 5, p. 4, 2006.

[Bibtex]`@article{8590957, abstract = {The Lieb-Robinson bound states that local Hamiltonian evolution in nonrelativistic quantum mechanical theories gives rise to the notion of an effective light cone with exponentially decaying tails. We discuss several consequences of this result in the context of quantum information theory. First, we show that the information that leaks out to spacelike separated regions is negligible and that there is a finite speed at which correlations and entanglement can be distributed. Second, we discuss how these ideas can be used to prove lower bounds on the time it takes to convert states without topological quantum order to states with that property. Finally, we show that the rate at which entropy can be created in a block of spins scales like the boundary of that block.}, articleno = {050401}, author = {Bravyi, S and Hastings, MB and Verstraete, Frank}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {5}, pages = {4}, title = {Lieb-Robinson bounds and the generation of correlations and topological quantum order}, url = {http://dx.doi.org/10.1103/PhysRevLett.97.050401}, volume = {97}, year = {2006}, }`

- M. M. Wolf, G. Ortiz, F. Verstraete, and I. J. Cirac, “Quantum phase transitions in matrix product systems,” PHYSICAL REVIEW LETTERS, vol. 97, iss. 11, p. 4, 2006.

[Bibtex]`@article{8588639, abstract = {We investigate quantum phase transitions (QPTs) in spin chain systems characterized by local Hamiltonians with matrix product ground states. We show how to theoretically engineer such QPT points between states with predetermined properties. While some of the characteristics of these transitions are familiar, like the appearance of singularities in the thermodynamic limit, diverging correlation length, and vanishing energy gap, others differ from the standard paradigm: In particular, the ground state energy remains analytic, and the entanglement entropy of a half-chain stays finite. Examples demonstrate that these kinds of transitions can occur at the triple point of {\textacutedbl}conventional{\textacutedbl} QPTs.}, articleno = {110403}, author = {Wolf, Michael M and Ortiz, Gerardo and Verstraete, Frank and Cirac, J Ignacio}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {11}, pages = {4}, title = {Quantum phase transitions in matrix product systems}, url = {http://dx.doi.org/10.1103/PhysRevLett.97.110403}, volume = {97}, year = {2006}, }`

- D. Porras, F. Verstraete, and J. Cirac, “Renormalization algorithm for the calculation of spectra of interacting quantum systems,” PHYSICAL REVIEW B, vol. 73, iss. 1, p. 7, 2006.

[Bibtex]`@article{8591035, abstract = {We present an algorithm for the calculation of eigenstates with definite linear momentum in quantum lattices. Our method is related to the density matrix renormalization group, and makes use of the distribution of multipartite entanglement to build variational wave functions with translational symmetry. The algorithm is applied to the study of bilinear-biquadratic S=1 chains, in particular to the region of phase space between the dimerized and ferromagnetic phases.}, articleno = {014410}, author = {Porras, D and Verstraete, Frank and Cirac, JI}, issn = {1098-0121}, journal = {PHYSICAL REVIEW B}, language = {eng}, number = {1}, pages = {7}, title = {Renormalization algorithm for the calculation of spectra of interacting quantum systems}, url = {http://dx.doi.org/10.1103/PhysRevB.73.014410}, volume = {73}, year = {2006}, }`

- F. Verstraete, M. Wolf, D. Perez-Garcia, and J. Cirac, “Criticality, the area law, and the computational power of projected entangled pair states,” PHYSICAL REVIEW LETTERS, vol. 96, iss. 22, p. 4, 2006.

[Bibtex]`@article{8590963, abstract = {The projected entangled pair state (PEPS) representation of quantum states on two-dimensional lattices induces an entanglement based hierarchy in state space. We show that the lowest levels of this hierarchy exhibit a very rich structure including states with critical and topological properties. We prove, in particular, that coherent versions of thermal states of any local 2D classical spin model correspond to such PEPS, which are in turn ground states of local 2D quantum Hamiltonians. This correspondence maps thermal onto quantum fluctuations, and it allows us to analytically construct critical quantum models exhibiting a strict area law scaling of the entanglement entropy in the face of power law decaying correlations. Moreover, it enables us to show that there exist PEPS which can serve as computational resources for the solution of NP-hard problems.}, articleno = {220601}, author = {Verstraete, Frank and Wolf, MM and Perez-Garcia, D and Cirac, JI}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {22}, pages = {4}, title = {Criticality, the area law, and the computational power of projected entangled pair states}, url = {http://dx.doi.org/10.1103/PhysRevLett.96.220601}, volume = {96}, year = {2006}, }`

- M. Popp, F. Verstraete, M. Martin-Delgado, and I. Cirac, “Numerical computation of localizable entanglement in spin chains,” APPLIED PHYSICS B-LASERS AND OPTICS, vol. 82, iss. 2, pp. 225-235, 2006.

[Bibtex]`@article{8590976, abstract = {We present an introduction to the concept of localizable entanglement (LE) with special focus on its numerical computation. LE is an entanglement measure for multipartite systems, which leads naturally to notions like entanglement length and entanglement fluctuations. After briefly reviewing basic properties of LE we present a scheme for the numerical calculation of LE. It is based on the matrix-product state representation of many-body quantum states and the Monte Carlo method. It can be applied both to pure and mixed states. Using this method we calculate the LE of ground and thermal states for various spin systems.}, author = {Popp, M and Verstraete, Frank and Martin-Delgado, MA and Cirac, I}, issn = {0946-2171}, journal = {APPLIED PHYSICS B-LASERS AND OPTICS}, language = {eng}, number = {2}, pages = {225--235}, title = {Numerical computation of localizable entanglement in spin chains}, url = {http://dx.doi.org/10.1007/s00340-005-2069-x}, volume = {82}, year = {2006}, }`

- S. Anders, M. Plenio, W. Duer, F. Verstraete, and H-J. Briegel, “Ground-state approximation for strongly interacting spin systems in arbitrary spatial dimension,” PHYSICAL REVIEW LETTERS, vol. 97, iss. 10, p. 4, 2006.

[Bibtex]`@article{8590951, abstract = {We introduce a variational method for the approximation of ground states of strongly interacting spin systems in arbitrary geometries and spatial dimensions. The approach is based on weighted graph states and superpositions thereof. These states allow for the efficient computation of all local observables (e.g., energy) and include states with diverging correlation length and unbounded multiparticle entanglement. As a demonstration, we apply our approach to the Ising model on 1D, 2D, and 3D square lattices. We also present generalizations to higher spins and continuous-variable systems, which allows for the investigation of lattice field theories.}, articleno = {107206}, author = {Anders, S and Plenio, MB and Duer, W and Verstraete, Frank and Briegel, H-J}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {10}, pages = {4}, title = {Ground-state approximation for strongly interacting spin systems in arbitrary spatial dimension}, url = {http://dx.doi.org/10.1103/PhysRevLett.97.10206}, volume = {97}, year = {2006}, }`

### 2005

- F. Verstraete, J. Cirac, J. Latorre, E. Rico, and M. Wolf, “Renormalization-group transformations on quantum states,” PHYSICAL REVIEW LETTERS, vol. 94, iss. 14, p. 4, 2005.

[Bibtex]`@article{8594021, abstract = {We construct a general renormalization-group transformation on quantum states, independent of any Hamiltonian dynamics of the system. We illustrate this procedure for translational invariant matrix product states in one dimension and show that product, Greenberger-Horne-Zeilinger, W, and domain wall states are special cases of an emerging classification of the fixed points of this coarse-graining transformation.}, articleno = {140601}, author = {Verstraete, Frank and Cirac, JI and Latorre, JI and Rico, E and Wolf, MM}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {14}, pages = {4}, title = {Renormalization-group transformations on quantum states}, url = {http://dx.doi.org/10.1103/PhysRevLett.94.140601}, volume = {94}, year = {2005}, }`

- K. Vollbrecht and F. Verstraete, “Interpolation of recurrence and hashing entanglement distillation protocols,” PHYSICAL REVIEW A, vol. 71, iss. 6, p. 7, 2005.

[Bibtex]`@article{8594017, abstract = {We construct interesting entanglement distillation protocols by interpolating between the recurrence and hashing protocols. This leads to asymptotic two-way distillation protocols, resulting in an improvement of the distillation rate for all mixed Bell diagonal entangled states, even for the ones with very high fidelity. We also present a method for how entanglement-assisted distillation protocol can be converted into nonentanglement-assisted protocols with the same yield.}, articleno = {062325}, author = {Vollbrecht, KGH and Verstraete, Frank}, issn = {1050-2947}, journal = {PHYSICAL REVIEW A}, language = {eng}, number = {6}, pages = {7}, title = {Interpolation of recurrence and hashing entanglement distillation protocols}, url = {http://dx.doi.org/10.1103/PhysRevA.71.062325}, volume = {71}, year = {2005}, }`

- T. Cubitt, F. Verstraete, and J. Cirac, “Entanglement flow in multipartite systems,” PHYSICAL REVIEW A, vol. 71, iss. 5, p. 12, 2005.

[Bibtex]`@article{8594019, abstract = {We investigate entanglement dynamics in multipartite systems, establishing a quantitative concept of entanglement flow: both flow through individual particles and flow along general networks of interacting particles. In the former case, the rate at which a particle can transmit entanglement is shown to depend on that particle's entanglement with the rest of the system. In the latter, we derive a set of entanglement rate equations, relating the rate of entanglement generation between two subsets of particles to the entanglement already present further back along the network. We use the rate equations to derive a lower bound on entanglement generation in qubit chains, and compare this to existing entanglement creation protocols.}, articleno = {052308}, author = {Cubitt, TS and Verstraete, Frank and Cirac, JI}, issn = {2469-9926}, journal = {PHYSICAL REVIEW A}, language = {eng}, number = {5}, pages = {12}, title = {Entanglement flow in multipartite systems}, url = {http://dx.doi.org/10.1103/PhysRevA.71.052308}, volume = {71}, year = {2005}, }`

- F. Verstraete and J. Cirac, “Mapping local Hamiltonians of fermions to local Hamiltonians of spins,” JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, p. 10, 2005.

[Bibtex]`@article{8594012, abstract = {We show how to map local fermionic problems onto local spin problems on a lattice in any dimension. The main idea is to introduce auxiliary degrees of freedom, represented by Majorana fermions, which allow us to extend the Jordan-Wigner transformation to dimensions higher than one. We also discuss the implications of our results in the numerical investigation of fermionic systems.}, articleno = {P09012}, author = {Verstraete, Frank and Cirac, JI}, issn = {1742-5468}, journal = {JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT}, language = {eng}, pages = {10}, title = {Mapping local Hamiltonians of fermions to local Hamiltonians of spins}, url = {http://dx.doi.org/10.1088/1742-5468/2005/09/P09012}, year = {2005}, }`

- V. Murg, F. Verstraete, and J. Cirac, “Efficient evaluation of partition functions of inhomogeneous many-body spin systems,” PHYSICAL REVIEW LETTERS, vol. 95, iss. 5, p. 4, 2005.

[Bibtex]`@article{8594015, abstract = {We present a numerical method to evaluate partition functions and associated correlation functions of inhomogeneous 2D classical spin systems and 1D quantum spin systems. The method is scalable and has a controlled error. We illustrate the algorithm by calculating the finite-temperature properties of bosonic particles in 1D optical lattices, as realized in current experiments.}, articleno = {057206}, author = {Murg, V and Verstraete, Frank and Cirac, JI}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {5}, pages = {4}, title = {Efficient evaluation of partition functions of inhomogeneous many-body spin systems}, url = {http://dx.doi.org/10.1103/PhysRevLett.95.057206}, volume = {95}, year = {2005}, }`

- B. Paredes, F. Verstraete, and J. Cirac, “Exploiting quantum parallelism to simulate quantum random many-body systems,” PHYSICAL REVIEW LETTERS, vol. 95, iss. 14, p. 4, 2005.

[Bibtex]`@article{8593970, abstract = {We present an algorithm that exploits quantum parallelism to simulate randomness in a quantum system. In our scheme, all possible realizations of the random parameters are encoded quantum mechanically in a superposition state of an auxiliary system. We show how our algorithm allows for the efficient simulation of dynamics of quantum random spin chains with known numerical methods. We propose an experimental realization based on atoms in optical lattices in which disorder could be simulated in parallel and in a controlled way through the interaction with another atomic species.}, articleno = {140501}, author = {Paredes, B and Verstraete, Frank and Cirac, JI}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {14}, pages = {4}, title = {Exploiting quantum parallelism to simulate quantum random many-body systems}, url = {http://dx.doi.org/10.1103/PhysRevLett.95.140501}, volume = {95}, year = {2005}, }`

- C. Schon, E. Solano, F. Verstraete, J. Cirac, and M. Wolf, “Sequential generation of entangled multiqubit states,” PHYSICAL REVIEW LETTERS, vol. 95, iss. 11, p. 4, 2005.

[Bibtex]`@article{8594010, abstract = {We consider the deterministic generation of entangled multiqubit states by the sequential coupling of an ancillary system to initially uncorrelated qubits. We characterize all achievable states in terms of classes of matrix-product states and give a recipe for the generation on demand of any multiqubit state. The proposed methods are suitable for any sequential generation scheme, though we focus on streams of single-photon time-bin qubits emitted by an atom coupled to an optical cavity. We show, in particular, how to generate familiar quantum information states such as W, Greenberger-Horne-Zeilinger, and cluster states within such a framework.}, articleno = {110503}, author = {Schon, C and Solano, E and Verstraete, Frank and Cirac, JI and Wolf, MM}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {11}, pages = {4}, title = {Sequential generation of entangled multiqubit states}, url = {http://dx.doi.org/10.1103/PhysRevLett.95.110503}, volume = {95}, year = {2005}, }`

- J. Smolin, F. Verstraete, and A. Winter, “Entanglement of assistance and multipartite state distillation,” PHYSICAL REVIEW A, vol. 72, iss. 5, p. 10, 2005.

[Bibtex]`@article{8593965, abstract = {We find that the asymptotic entanglement of assistance of a general bipartite mixed state is equal to the smaller of its two local entropies. Our protocol gives rise to the asymptotically optimal Einstein-Podolsky-Rosen (EPR) pair distillation procedure for a given tripartite pure state, and we show that it actually yields EPR and Greenberger-Horne-Zeilinger (GHZ) states; in fact, under a restricted class of protocols, which we call {\textacutedbl}one-way broadcasting,{\textacutedbl} the GHZ rate is shown to be optimal. This result implies a capacity theorem for quantum channels where the environment helps transmission by broadcasting the outcome of an optimally chosen measurement. We discuss generalizations to m parties and show (for m=4) that the maximal amount of entanglement that can be localized between two parties is given by the smallest entropy of a group of parties of which the one party is a member, but not the other. This gives an explicit expression for the asymptotic localizable entanglement and shows that any nontrivial ground state of a spin system can be used as a perfect quantum repeater if many copies are available in parallel. Finally, we provide evidence that any unital channel is asymptotically equivalent to a mixture of unitaries and any general channel to a mixture of partial isometries.}, articleno = {052317}, author = {Smolin, JA and Verstraete, Frank and Winter, A}, issn = {2469-9926}, journal = {PHYSICAL REVIEW A}, language = {eng}, number = {5}, pages = {10}, title = {Entanglement of assistance and multipartite state distillation}, url = {http://dx.doi.org/10.1103/PhysRevA.72.052317}, volume = {72}, year = {2005}, }`

- M. Popp, F. Verstraete, M. Martin-Delgado, and J. Cirac, “Localizable entanglement,” PHYSICAL REVIEW A, vol. 71, iss. 4, p. 18, 2005.

[Bibtex]`@article{8594023, abstract = {We consider systems of interacting spins and study the entanglement that can be localized, on average, between two separated spins by performing local measurements on the remaining spins. This concept of localizable entanglement (LE) leads naturally to notions like entanglement length and entanglement fluctuations. For both spin-1/2 and spin-1 systems, we prove that the LE of a pure quantum state can be lower bounded by connected correlation functions. We further propose a scheme, based on matrix-product states and the Monte Carlo method, to efficiently calculate the LE for quantum states of a large number of spins. The virtues of LE are illustrated for various spin models. In particular, characteristic features of a quantum phase transition such as a diverging entanglement length can be observed. We also give examples for pure quantum states exhibiting a diverging entanglement length but finite correlation length. We have numerical evidence that the ground state of the antiferromagnetic spin-1 Heisenberg chain can serve as a perfect quantum channel. Furthermore, we apply the numerical method to mixed states and study the entanglement as a function of temperature.}, articleno = {042306}, author = {Popp, M and Verstraete, Frank and Martin-Delgado, MA and Cirac, JI}, issn = {1050-2947}, journal = {PHYSICAL REVIEW A}, language = {eng}, number = {4}, pages = {18}, title = {Localizable entanglement}, url = {http://dx.doi.org/10.1103/PhysRevA.71.042306}, volume = {71}, year = {2005}, }`

### 2004

- F. Verstraete, D. Porras, and J. Cirac, “Density matrix renormalization group and periodic boundary conditions : a quantum information perspective,” PHYSICAL REVIEW LETTERS, vol. 93, iss. 22, p. 4, 2004.

[Bibtex]`@article{8594032, abstract = {We introduce a picture to analyze the density matrix renormalization group (DMRG) numerical method from a quantum information perspective. This leads to a variational formulation of DMRG which allows for dramatic improvements in the case of problems with periodic boundary conditions. The picture also explains some features of the method in terms of entanglement and teleportation.}, articleno = {227205}, author = {Verstraete, Frank and Porras, D and Cirac, JI}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {22}, pages = {4}, title = {Density matrix renormalization group and periodic boundary conditions : a quantum information perspective}, url = {http://dx.doi.org/10.1103/PhysRevLett.93.227205}, volume = {93}, year = {2004}, }`

- E. Briand, J. Luque, J. Thibon, and F. Verstraete, “The moduli space of three-qutrit states,” JOURNAL OF MATHEMATICAL PHYSICS, vol. 45, iss. 12, pp. 4855-4867, 2004.

[Bibtex]`@article{8594025, author = {Briand, E and Luque, JG and Thibon, JY and Verstraete, Frank}, issn = {0022-2488}, journal = {JOURNAL OF MATHEMATICAL PHYSICS}, language = {eng}, number = {12}, pages = {4855--4867}, title = {The moduli space of three-qutrit states}, url = {http://dx.doi.org/10.1063/1.1809255}, volume = {45}, year = {2004}, }`

- F. Verstraete, M. Martin-Delgado, and J. Cirac, “Diverging entanglement length in gapped quantum spin systems,” PHYSICAL REVIEW LETTERS, vol. 92, iss. 8, p. 4, 2004.

[Bibtex]`@article{8594042, abstract = {We prove the existence of gapped quantum Hamiltonians whose ground states exhibit an infinite entanglement length, as opposed to their finite correlation length. Using the concept of entanglement swapping, the localizable entanglement is calculated exactly for valence bond and finitely correlated states, and the existence of the so-called string-order parameter is discussed. We also report on evidence that the ground state of an antiferromagnetic chain can be used as a perfect quantum channel if local measurements on the individual spins can be implemented.}, articleno = {087201}, author = {Verstraete, Frank and Martin-Delgado, MA and Cirac, JI}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {8}, pages = {4}, title = {Diverging entanglement length in gapped quantum spin systems}, url = {http://dx.doi.org/10.1103/PhysRevLett.92.087201}, volume = {92}, year = {2004}, }`

- N. Schuch, F. Verstraete, and J. Cirac, “Nonlocal resources in the presence of superselection rules,” PHYSICAL REVIEW LETTERS, vol. 92, iss. 8, p. 4, 2004.

[Bibtex]`@article{8594038, abstract = {Superselection rules severly alter the possible operations that can be implemented on a distributed quantum system. Whereas the restriction to local operations imposed by a bipartite setting gives rise to the notion of entanglement as a nonlocal resource, the superselection rule associated with particle number conservation leads to a new resource, the superselection induced variance of the local particle number. We show that, in the case of pure quantum states, one can quantify the nonlocal properties by only two additive measures, and that all states with the same measures can be asymptotically interconverted into each other by local operations and classical communication. Furthermore we discuss how superselection rules affect the concepts of majorization, teleportation, and mixed state entanglement.}, articleno = {087904}, author = {Schuch, N and Verstraete, Frank and Cirac, JI}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {8}, pages = {4}, title = {Nonlocal resources in the presence of superselection rules}, url = {http://dx.doi.org/10.1103/PhysRevLett.92.087904}, volume = {92}, year = {2004}, }`

- A. Miyake and F. Verstraete, “Multipartite entanglement in 2 x 2 x n quantum systems,” PHYSICAL REVIEW A, vol. 69, iss. 1, p. 9, 2004.

[Bibtex]`@article{8594055, abstract = {We classify multipartite entangled states in the Hilbert space H=C-2 x C-2 x C-n (ngreater than or equal to4), for example, the four-qubit system distributed over three parties, under local filtering operations. We show that there exist nine essentially different classes of states, giving rise to a five-graded partially ordered structure, including the celebrated Greenberger-Home-Zeilinger and W classes of three qubits. In particular, all 2 X 2 X n states can be deterministically prepared from one maximally entangled state, and some applications such as entanglement swapping are discussed.}, articleno = {012101}, author = {Miyake, A and Verstraete, Frank}, issn = {2469-9926}, journal = {PHYSICAL REVIEW A}, language = {eng}, number = {1}, pages = {9}, title = {Multipartite entanglement in 2 x 2 x n quantum systems}, url = {http://dx.doi.org/10.1103/PhysRevA.69.012101}, volume = {69}, year = {2004}, }`

- F. Verstraete, M. Popp, and J. Cirac, “Entanglement versus correlations in spin systems,” PHYSICAL REVIEW LETTERS, vol. 92, iss. 2, p. 4, 2004.

[Bibtex]`@article{8594047, abstract = {We consider pure quantum states of N{\textrangle}1 spins or qubits and study the average entanglement that can be localized between two separated spins by performing local measurements on the other individual spins. We show that all classical correlation functions provide lower bounds to this localizable entanglement, which follows from the observation that classical correlations can always be increased by doing appropriate local measurements on the other qubits. We analyze the localizable entanglement in familiar spin systems and illustrate the results on the hand of the Ising spin model, in which we observe characteristic features for a quantum phase transition such as a diverging entanglement length.}, articleno = {027901}, author = {Verstraete, Frank and Popp, M and Cirac, JI}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {2}, pages = {4}, title = {Entanglement versus correlations in spin systems}, url = {http://dx.doi.org/10.1103/PhysRevLett.92.027901}, volume = {92}, year = {2004}, }`

- F. Verstraete and J. Cirac, “Valence-bond states for quantum computation,” PHYSICAL REVIEW A, vol. 70, iss. 6, p. 4, 2004.

[Bibtex]`@article{8594027, abstract = {We propose a way of universal quantum computation by doing joint measurements on distributed singlets. We show how these joint measurements become local measurements when the singlets are interpreted as the virtual components of a large valence-bond state. This proves the equivalence of the cluster-state-based quantum computational model and the teleportation-based model, and we discuss several features and possible extensions. We show that all stabilizer states have a very simple interpretation in terms of valence-bond solids, which allows to understand their entanglement properties in a transparent way.}, articleno = {060302}, author = {Verstraete, Frank and Cirac, JI}, issn = {1050-2947}, journal = {PHYSICAL REVIEW A}, language = {eng}, number = {6}, pages = {4}, title = {Valence-bond states for quantum computation}, url = {http://dx.doi.org/10.1103/PhysRevA.70.060302}, volume = {70}, year = {2004}, }`

- F. Verstraete, J. Garcia-Ripoll, and J. Cirac, “Matrix product density operators : simulation of finite-temperature and dissipative systems,” PHYSICAL REVIEW LETTERS, vol. 93, iss. 20, p. 4, 2004.

[Bibtex]`@article{8594034, abstract = {We show how to simulate numerically the evolution of 1D quantum systems under dissipation as well as in thermal equilibrium. The method applies to both finite and inhomogeneous systems, and it is based on two ideas: (a) a representation for density operators which extends that of matrix product states to mixed states; (b) an algorithm to approximate the evolution (in real or imaginary time) of matrix product states which is variational.}, articleno = {207204}, author = {Verstraete, Frank and Garcia-Ripoll, JJ and Cirac, JI}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {20}, pages = {4}, title = {Matrix product density operators : simulation of finite-temperature and dissipative systems}, url = {http://dx.doi.org/10.1103/PhysRevLett.93.207204}, volume = {93}, year = {2004}, }`

- M. Wolf, F. Verstraete, and J. Cirac, “Entanglement frustration for Gaussian states on symmetric graphs,” PHYSICAL REVIEW LETTERS, vol. 92, iss. 8, p. 4, 2004.

[Bibtex]`@article{8594044, abstract = {We investigate the entanglement properties of multimode Gaussian states, which have some symmetry with respect to the ordering of the modes. We show how the symmetry constrains the entanglement between two modes of the system. In particular, we determine the maximal entanglement of formation that can be achieved in symmetric graphs like chains, 2D and 3D lattices, mean field models and the platonic solids. The maximal entanglement is always attained for the ground state of a particular quadratic Hamiltonian. The latter thus yields the maximal entanglement among all quadratic Hamiltonians having the considered symmetry.}, articleno = {087903}, author = {Wolf, MM and Verstraete, Frank and Cirac, JI}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {8}, pages = {4}, title = {Entanglement frustration for Gaussian states on symmetric graphs}, url = {http://dx.doi.org/10.1103/PhysRevLett.92.087903}, volume = {92}, year = {2004}, }`

- N. Schuch, F. Verstraete, and J. Cirac, “Quantum entanglement theory in the presence of superselection rules,” PHYSICAL REVIEW A, vol. 70, iss. 4, p. 15, 2004.

[Bibtex]`@article{8594036, abstract = {Superselection rules severely constrain the operations which can be implemented on a distributed quantum system. While the restriction to local operations and classical communication gives rise to entanglement as a nonlocal resource, particle number conservation additionally confines the possible operations and should give rise to a new resource. In Phys. Rev. Lett. 92, 087904 (2004) we showed that this resource can be quantified by a sin-le additional number, the superselection-induced variance (SIV), without changing the concept of entanglement. In this paper, we give the results on pure states in greater detail; additionally, we provide a discussion of mixed-state nonlocality with superselection rules where we consider both formation and distillation. Finally, we demonstrate that SIV is indeed a resource, i.e., that it captures how well a state can be used to overcome the restrictions imposed by the superselection rule.}, articleno = {042310}, author = {Schuch, N and Verstraete, Frank and Cirac, JI}, issn = {1050-2947}, journal = {PHYSICAL REVIEW A}, language = {eng}, number = {4}, pages = {15}, title = {Quantum entanglement theory in the presence of superselection rules}, url = {http://dx.doi.org/10.1103/PhysRevA.70.042310}, volume = {70}, year = {2004}, }`

### 2003

- T. Wei, K. Nemoto, P. Goldbart, P. Kwiat, W. Munro, and F. Verstraete, “Maximal entanglement versus entropy for mixed quantum states,” PHYSICAL REVIEW A, vol. 67, iss. 2, p. 12, 2003.

[Bibtex]`@article{8594069, abstract = {Maximally entangled mixed states are those states that, for a given mixedness, achieve the greatest possible entanglement. For two-qubit systems and for various combinations of entanglement and mixedness measures, the form of the corresponding maximally entangled mixed states is determined primarily analytically. As measures of entanglement, we consider entanglement of formation, relative entropy of entanglement, and negativity; as measures of mixedness, we consider linear and von Neumann entropies. We show that the forms of the maximally entangled mixed states can vary with the combination of (entanglement and mixedness) measures chosen. Moreover, for certain combinations, the forms of the maximally entangled mixed states can change discontinuously at a specific value of the entropy. Along the way, we determine the states that, for a given value of entropy, achieve maximal violation of Bell's inequality.}, articleno = {022110}, author = {Wei, TC and Nemoto, K and Goldbart, PM and Kwiat, PG and Munro, WJ and Verstraete, Frank}, issn = {2469-9926}, journal = {PHYSICAL REVIEW A}, language = {eng}, number = {2}, pages = {12}, title = {Maximal entanglement versus entropy for mixed quantum states}, url = {http://dx.doi.org/10.1103/PhysRevA.67.022110}, volume = {67}, year = {2003}, }`

- J. Dehaene, M. Van den Nest, B. De Moor, and F. Verstraete, “Local permutations of products of Bell states and entanglement distillation,” PHYSICAL REVIEW A, vol. 67, iss. 2, p. 6, 2003.

[Bibtex]`@article{8594067, abstract = {We present different algorithms for mixed-state multicopy entanglement distillation for pairs of qubits. Our algorithms perform significantly better than the best-known algorithms. Better algorithms can be derived that are tuned for specific initial states. These algorithms are based on a characterization of the group of all locally realizable permutations of the 4(n) possible tensor products of n Bell states.}, articleno = {022310}, author = {Dehaene, J and Van den Nest, M and De Moor, B and Verstraete, Frank}, issn = {1050-2947}, journal = {PHYSICAL REVIEW A}, language = {eng}, number = {2}, pages = {6}, title = {Local permutations of products of Bell states and entanglement distillation}, url = {http://dx.doi.org/10.1103/PhysRevA.67.022310}, volume = {67}, year = {2003}, }`

- T. Wei, K. Nemoto, P. M. Goldbart, P. G. Kwiat, W. J. Munro, and F. Verstraete, “Two-qubit mixed states and the entanglement-entropy frontier,” in Quantum communication, measurement and computing, Proceedings, 2003, pp. 37-40.

[Bibtex]`@inproceedings{8594073, abstract = {Maximally-entangled mixed states are states that, for a given mixedness (entropy), achieve the greatest possible entanglement. For two-qubit systems and for various combinations of entanglement and mixedness measures, we determine the form of the corresponding maximally-entangled mixed states analytically. We show that their forms can vary with the combination of entanglement and mixedness measures chosen. Moreover, for certain combinations, the forms of the maximally-entangled mixed states can change discontinuously at a specific value of the entropy.}, author = {Wei, Tzu-Chieh and Nemoto, Kae and Goldbart, Paul M and Kwiat, Paul G and Munro, William J and Verstraete, Frank}, booktitle = {Quantum communication, measurement and computing, Proceedings}, editor = {Shapiro, JH and Hirota, O}, isbn = {9781589490307}, language = {eng}, location = {Cambridge, MA, USA}, pages = {37--40}, publisher = {Rinton Press}, title = {Two-qubit mixed states and the entanglement-entropy frontier}, year = {2003}, }`

- F. Verstraete, J. Dehaene, and B. De Moor, “Normal forms and entanglement measures for multipartite quantum states,” PHYSICAL REVIEW A, vol. 68, iss. 1, p. 7, 2003.

[Bibtex]`@article{8594061, abstract = {A general mathematical framework is presented to describe local equivalence classes of multipartite quantum states under the action of local unitary and local filtering operations. This yields multipartite generalizations of the singular value decomposition. The analysis naturally leads to the introduction of entanglement measures quantifying the multipartite entanglement (as generalizations of the concurrence for two qubits and the 3-tangle for three qubits), and the optimal local filtering operations maximizing these entanglement monotones are obtained. Moreover, a natural extension of the definition of Greenberger-Horne-Zeilinger states to, e.g., 2x2xN systems is obtained.}, articleno = {012103}, author = {Verstraete, Frank and Dehaene, J and De Moor, B}, issn = {1050-2947}, journal = {PHYSICAL REVIEW A}, language = {eng}, number = {1}, pages = {7}, title = {Normal forms and entanglement measures for multipartite quantum states}, url = {http://dx.doi.org/10.1103/PhysRevA.68.012103}, volume = {68}, year = {2003}, }`

- F. Verstraete and H. Verschelde, “Optimal teleportation with a mixed state of two qubits,” PHYSICAL REVIEW LETTERS, vol. 90, iss. 9, p. 4, 2003.

[Bibtex]`@article{288582, abstract = {We consider a single copy of a mixed state of two qubits and derive the optimal trace-preserving local operations assisted by classical communication such as to maximize the fidelity of teleportation that can be achieved with this state. These optimal local operations turn out to be implementable by one-way communication and always yield a teleportation fidelity larger than 2/3 if the original state is entangled. This maximal achievable fidelity is an entanglement measure and turns out quantifying the minimal amount of mixing required to destroy the entanglement in a quantum state.}, articleno = {097901}, author = {Verstraete, Frank and Verschelde, Henri}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {9}, pages = {4}, title = {Optimal teleportation with a mixed state of two qubits}, url = {http://dx.doi.org/10.1103/PhysRevLett.90.097901}, volume = {90}, year = {2003}, }`

- F. Verstraete and J. Cirac, “Quantum nonlocality in the presence of superselection rules and data hiding protocols,” PHYSICAL REVIEW LETTERS, vol. 91, iss. 1, p. 4, 2003.

[Bibtex]`@article{8594059, abstract = {We consider a quantum system subject to superselection rules, for which certain restrictions apply to the quantum operations that can be implemented. It is shown how the notion of quantum nonlocality has to be redefined in the presence of superselection rules: there exist separable states that cannot be prepared locally and exhibit some form of nonlocality. Moreover, the notion of local distinguishability in the presence of classical communication has to be altered. This can be used to perform quantum information tasks that are otherwise impossible. In particular, this leads to the introduction of perfect quantum data hiding protocols, for which quantum communication (eventually in the form of a separable but nonlocal state) is needed to unlock the secret.}, articleno = {010404}, author = {Verstraete, Frank and Cirac, JI}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {1}, pages = {4}, title = {Quantum nonlocality in the presence of superselection rules and data hiding protocols}, url = {http://dx.doi.org/10.1103/PhysRevLett.91.010404}, volume = {91}, year = {2003}, }`

- M. M. Wolf, F. Verstraete, and I. J. Cirac, “Entanglement and frustration in ordered systems,” INTERNATIONAL JOURNAL OF QUANTUM INFORMATION, vol. 1, iss. 4, pp. 465-477, 2003.

[Bibtex]`@article{8588635, abstract = {This article reviews and extends recent results concerning entanglement and frustration in multipartite systems which have some symmetry with respect to the ordering of the particles. Starting point of the discussion are Bell inequalities: their relation to frustration in classical systems and their satisfaction for quantum states which have a symmetric extension. We then discussed how more general global symmetries of multipartite systems constrain the entanglement between two neighboring particles. We prove that maximal entanglement (measured in terms of the entanglement of formation) is always attained for the ground state of a certain nearest neighbor interaction Hamiltonian having the considered symmetry with the achievable amount of entanglement being a function of the ground state energy. Systems of Gaussian states, i.e. quantum harmonic oscillators, are investigated in more detail and the results are compared to what is known about ordered qubit systems.}, author = {Wolf, Michael M and Verstraete, Frank and Cirac, J Ignacio}, issn = {0219-7499}, journal = {INTERNATIONAL JOURNAL OF QUANTUM INFORMATION}, language = {eng}, number = {4}, pages = {465--477}, title = {Entanglement and frustration in ordered systems}, url = {http://dx.doi.org/10.1142/S021974990300036X}, volume = {1}, year = {2003}, }`

- T. Laustsen, F. Verstraete, and S. Van Enk, “Local vs. joint measurements for the entanglement of assistance,” QUANTUM INFORMATION & COMPUTATION, vol. 3, iss. 1, pp. 64-83, 2003.

[Bibtex]`@article{8594075, abstract = {We consider a variant of the entanglement of assistance, as independently introduced by D.P. DiVincenzo et al. (quart-ph/9803033) and O. Cohen (Phys. Rev. Lett. 80, 2493 (1998)). Instead of considering three-party states in which one of the parties, the assistant, performs a measurement such that the remaining two parties are left with on average as much entanglement as possible, we consider four-party states where two parties play the role of assistants. We answer several questions that arise naturally in this scenario, such as (i) how much more entanglement can be produced when the assistants are allowed to perform joint measurements, (ii) for what type of states are local measurements sufficient, (iii) is it necessary for the second assistant to know the measurement outcome of the first, and (iv) are projective measurements sufficient or are more general POVMs needed?.}, author = {Laustsen, T and Verstraete, Frank and Van Enk, SJ}, issn = {1533-7146}, journal = {QUANTUM INFORMATION \& COMPUTATION}, language = {eng}, number = {1}, pages = {64--83}, title = {Local vs. joint measurements for the entanglement of assistance}, volume = {3}, year = {2003}, }`

- T. Cubitt, F. Verstraete, W. Dur, and J. Cirac, “Separable states can be used to distribute entanglement,” PHYSICAL REVIEW LETTERS, vol. 91, iss. 3, p. 4, 2003.

[Bibtex]`@article{8594057, abstract = {We show that no entanglement is necessary to distribute entanglement; that is, two distant particles can be entangled by sending a third particle that is never entangled with the other two. Similarly, two particles can become entangled by continuous interaction with a highly mixed mediating particle that never itself becomes entangled. We also consider analogous properties of completely positive maps, in which the composition of two separable maps can create entanglement.}, articleno = {037902}, author = {Cubitt, TS and Verstraete, Frank and Dur, W and Cirac, JI}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {3}, pages = {4}, title = {Separable states can be used to distribute entanglement}, url = {http://dx.doi.org/10.1103/PhysRevLett.91.037902}, volume = {91}, year = {2003}, }`

- A. Childs, D. Leung, F. Verstraete, and G. Vidal, “Asymptotic entanglement capacity of the Ising and anisotropic Heisenberg interactions,” QUANTUM INFORMATION & COMPUTATION, vol. 3, iss. 2, pp. 97-105, 2003.

[Bibtex]`@article{8594065, abstract = {We calculate the asymptotic entanglement capacity of the Ising interaction sigma(z) circle times sigma(z), the anisotropic Heisenberg interaction sigma(x) circle times sigma(x) + sigma(y) circle times sigma(y), and more generally, any two-qubit Hamiltonian with canonical form K = mu(x) sigma(x) circle times sigma(x) + mu(y) sigma(y) circle times sigma(y).We also describe an entanglement assisted classical communication protocol using the Hamiltonian K with rate equal to the asymptotic entanglement capacity.}, author = {Childs, AM and Leung, DW and Verstraete, Frank and Vidal, G}, issn = {1533-7146}, journal = {QUANTUM INFORMATION \& COMPUTATION}, language = {eng}, number = {2}, pages = {97--105}, title = {Asymptotic entanglement capacity of the Ising and anisotropic Heisenberg interactions}, url = {http://dx.doi.org/10.26421/QIC3.2}, volume = {3}, year = {2003}, }`

### 2002

- F. Verstraete and H. Verschelde, “Optimal enhancement of the fidelity of two qubits.,” PHYSICAL REVIEW A, vol. 66, iss. 022307, pp. 1-5, 2002.

[Bibtex]`@article{162091, author = {Verstraete, Frank and Verschelde, Henri}, issn = {1050-2947}, journal = {PHYSICAL REVIEW A}, language = {eng}, number = {022307}, pages = {1--5}, title = {Optimal enhancement of the fidelity of two qubits.}, volume = {66}, year = {2002}, }`

- F. Verstraete and H. Verschelde, “Fidelity of mixed states of two qubits,” PHYSICAL REVIEW A, vol. 66, iss. 2, p. 5, 2002.

[Bibtex]`@article{8594083, abstract = {We consider a single copy of a mixed state of two qubits and show how its fidelity or maximal singlet fraction is related to the entanglement measures concurrence and negativity. We characterize the extreme points of a convex set of states with constant fidelity, and use this to prove tight lower and upper bounds on the fidelity for a given amount of entanglement.}, articleno = {022307}, author = {Verstraete, Frank and Verschelde, Henri}, issn = {1050-2947}, journal = {PHYSICAL REVIEW A}, language = {eng}, number = {2}, pages = {5}, title = {Fidelity of mixed states of two qubits}, url = {http://dx.doi.org/10.1103/PhysRevA.66.022307}, volume = {66}, year = {2002}, }`

- F. Verstraete, J. Dehaene, B. De Moor, and H. Verschelde, “Four qubits can be entangled in nine different ways,” PHYSICAL REVIEW A, vol. 65, iss. 5, p. 5, 2002.

[Bibtex]`@article{162087, abstract = {We consider a single copy of a pure four-partite state of qubits and investigate its behavior under the action of stochastic local quantum operations assisted by classical communication (SLOCC). This leads to a complete classification of all different classes of pure states of four qubits. It is shown that there exist nine families of states corresponding to nine different ways of entangling four qubits. The states in the generic family give rise to Greenberger-Horne-Zeilinger-like entanglement. The other ones contain essentially two-or three-qubit entanglement distributed among the four parties. The concept of concurrence and 3-tangle is generalized to the case of mixed states of four qubits, giving rise to a seven-parameter family of entanglement monotones. Finally, the SLOCC operations maximizing all these entanglement monotones are derived, yielding the optimal single-copy distillation protocol.}, articleno = {052112}, author = {Verstraete, Frank and Dehaene, J and De Moor, B and Verschelde, Henri}, issn = {1050-2947}, journal = {PHYSICAL REVIEW A}, language = {eng}, number = {5}, pages = {5}, title = {Four qubits can be entangled in nine different ways}, url = {http://dx.doi.org/10.1103/PhysRevA.65.052112}, volume = {65}, year = {2002}, }`

- F. Verstraete and M. Wolf, “Entanglement versus Bell violations and their behaviour under local filtering operations,” PHYSICAL REVIEW LETTERS, vol. 89, iss. 17, p. 4, 2002.

[Bibtex]`@article{8594079, abstract = {We discuss the relations between the violation of the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality for systems of two qubits on the one side and entanglement of formation, local filtering operations, and the entropy and purity on the other. We calculate the extremal Bell violations for a given amount of entanglement of formation and characterize the respective states, which turn out to have extremal properties also with respect to the entropy, purity, and several entanglement monotones. The optimal local filtering operations leading to the maximal Bell violation for a given state are provided, and the special role of the resulting Bell diagonal states in the context of Bell inequalities is discussed.}, articleno = {170401}, author = {Verstraete, Frank and Wolf, MM}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, language = {eng}, number = {17}, pages = {4}, title = {Entanglement versus Bell violations and their behaviour under local filtering operations}, url = {http://dx.doi.org/10.1103/PhysRevLett.89.170401}, volume = {89}, year = {2002}, }`

- F. Verstraete, J. Dehaene, and B. De Moor, “On the geometry of entangled states,” JOURNAL OF MODERN OPTICS, vol. 49, iss. 8, pp. 1277-1287, 2002.

[Bibtex]`@article{8594088, abstract = {The basic question that is addressed in this paper is finding the closest separable state for a given entangled state, measured with the Hilbert-Schmidt distance. While this problem is in general very difficult, we show that the following strongly related problem can be solved: find the Hilbert-Schmidt distance of an entangled state to the set of all partially transposed states. We prove that this latter distance can be expressed as a function of the negative eigenvalues of the partial transpose of the entangled state, and show how it is related to the distance of a state to the set of positive, partially transposed (PPT) states. We illustrate this by calculating the closest biseparable state to the W state and give a simple and very general proof for the fact that the set of W-type states is not of measure zero. Next we show that all surfaces with states whose partial transposes have constant minimal negative eigenvalue are similar to the boundary of PPT states. We illustrate this with some examples on bipartite qubit states, where contours of constant negativity are plotted on two-dimensional intersections of the complete state space.}, author = {Verstraete, Frank and Dehaene, J and De Moor, B}, issn = {0950-0340}, journal = {JOURNAL OF MODERN OPTICS}, language = {eng}, location = {Gdansk, Poland}, number = {8}, pages = {1277--1287}, title = {On the geometry of entangled states}, url = {http://dx.doi.org/10.1080/09500340110115488}, volume = {49}, year = {2002}, }`

- F. Verstraete, “A study of entanglement in quantum information theory,” PhD Thesis, 2002.

[Bibtex]`@phdthesis{8603813, abstract = {Although the concept of quantum entanglement has been known for about seventy years, it only recently quit the realms of meta-theoretical discussions when it was discovered how entanglement can be exploited to compute and communicate with an unprecedented power. The primary motivation of the work presented in this thesis has been to contribute to the big effort that has been done during the last decade to understand and quantify quantum en- tanglement. We have developed advanced techniques of linear and multilinear algebra to investigate and classify entangled pure and mixed quantum states, and discussed some novel applications in the field of quantum information theory. The results presented in this thesis are mainly of interest from a fundamental point a view: entanglement is the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought [186]. It is however a real privilege that fundamental research in quantum information theory bears the tools of tomorrow{\textquoteright}s electrical engineers: the ongoing minia- turization of electronic components will soon reach a scale where quantum mechanical effects play a major role. The first part of this thesis is devoted to the study of entanglement. Local equivalence classes of multipartite pure and mixed quantum systems are dis- cussed, and different entanglement measures are introduced and compared. The second part is mainly concerned with the problem of transmission and extraction of classical and quantum information through quantum channels. Optimal detection strategies for continuously monitored systems are derived, and we exploit a duality between quantum maps and entangled quantum states to present a unified description of quantum channels.}, author = {Verstraete, Frank}, isbn = {9789056823771}, language = {eng}, pages = {XXIV, 242}, publisher = {Katholieke Universiteit Leuven. Faculteit Toegepaste Wetenschappen}, title = {A study of entanglement in quantum information theory}, year = {2002}, }`

- F. Verstraete, J. Dehaene, and B. De Moor, “Lorentz singular-value decomposition and its applications to pure states of three qubits,” PHYSICAL REVIEW A, vol. 65, iss. 3, p. 6, 2002.

[Bibtex]`@article{8594092, abstract = {All mixed states of two qubits can be brought into normal form by the action of local operations and classical communication operations of the kind rho'=(AxB) rho(AxB)dagger. These normal forms can be obtained by considering a Lorentz singular-value decomposition on a real parametrization of the density matrix. We show that the Lorentz singular values are variationally defined and give rise to entanglement monotones, with as a special case the concurrence. Next a necessary and sufficient criterion is conjectured for a mixed state to be convertible into another specific one with a nonzero probability. Finally the formalism of the Lorentz singular-value decomposition is applied to tripartite pure states of qubits. New proofs are given for the existence of the Greenberger-Horne-Zeilinger (GHZ) class and W class of states, and a rigorous proof for the optimal distillation of a GHZ state is derived.}, articleno = {032308}, author = {Verstraete, Frank and Dehaene, J and De Moor, B}, issn = {2469-9926}, journal = {PHYSICAL REVIEW A}, language = {eng}, number = {3}, pages = {6}, title = {Lorentz singular-value decomposition and its applications to pure states of three qubits}, url = {http://dx.doi.org/10.1103/PhysRevA.65.032308}, volume = {65}, year = {2002}, }`

### 2001

- F. Verstraete, A. Doherty, and H. Mabuchi, “Sensitivity optimization in quantum parameter estimation,” PHYSICAL REVIEW A, vol. 64, iss. 3, p. 12, 2001.

[Bibtex]`@article{137530, abstract = {We present a general framework for sensitivity optimization in quantum parameter estimation schemes based on continuous (indirect) observation of a dynamical system. As an illustrative example, we analyze the canonical scenario of monitoring the position of a free mass or harmonic oscillator to detect weak classical forces. We show that our framework allows the consideration of sensitivity scheduling, as well as estimation strategies for nonstationary signals, leading us to propose corresponding generalizations of the standard quantum limit for force detection.}, articleno = {032111}, author = {Verstraete, Frank and Doherty, AC and Mabuchi, H}, issn = {1050-2947}, journal = {PHYSICAL REVIEW A}, language = {eng}, number = {3}, pages = {12}, title = {Sensitivity optimization in quantum parameter estimation}, url = {http://dx.doi.org/10.1103/PhysRevA.64.032111}, volume = {64}, year = {2001}, }`

- F. Verstraete, K. Audenaert, and B. De Moor, “Maximally entangled mixed states of two qubits,” PHYSICAL REVIEW A, vol. 64, iss. 1, 2001.

[Bibtex]`@article{137526, abstract = {We consider mixed states of two qubits and show under which global unitary operations their entanglement is maximized. This leads to a class of states that is a generalization of the Bell states. Three measures of entanglement are considered: entanglement of formation, negativity, and relative entropy of entanglement. Surprisingly all states that maximize one measure also maximize the; others. We give a complete characterization of these generalized Bell states and prove that these states for fixed eigenvalues are all equivalent under local unitary transformations. Furthermore we characterize all nearly entangled states closest to the maximally mixed state and derive a lower bound on the volume of separable mixed states.}, articleno = {012316}, author = {Verstraete, Frank and Audenaert, Koenraad and De Moor, Bart}, issn = {1050-2947}, journal = {PHYSICAL REVIEW A}, language = {eng}, number = {1}, title = {Maximally entangled mixed states of two qubits}, url = {http://dx.doi.org/10.1103/PhysRevA.64.012316}, volume = {64}, year = {2001}, }`

- K. Audenaert, F. Verstraete, and B. De Moor, “Variational characterisations in quantum parameter estimation,” PHYSICAL REVIEW A, vol. 64, iss. 5, p. 13, 2001.

[Bibtex]`@article{137484, abstract = {In this paper we develop a mathematical framework for the characterization of separability and entanglement of formation (EOF) of general bipartite states. These characterizations are variational in nature, meaning that separability and EOF are given in terms of a function that is to be minimized over the manifold of unitary matrices. A major benefit of such a characterization is that it directly leads to a numerical procedure for calculating EOF. We present an efficient minimization algorithm and apply it to the bound entangled 3 x 3 Horodecki states: we show that their EOF is very low and that their distance to the set of separable states is also very small. Within the same variational framework we rephrase the results by Wootters [W. Wootters. Phys. Rev. Lett. 80, 2245 (1998)] on EOF for 2 x 2 states and also present some progress in generalizing these results to higher-dimensional systems.}, articleno = {052304}, author = {Audenaert, Koenraad and Verstraete, Frank and De Moor, Bart}, issn = {1050-2947}, journal = {PHYSICAL REVIEW A}, language = {eng}, number = {5}, pages = {13}, title = {Variational characterisations in quantum parameter estimation}, url = {http://dx.doi.org/10.1103/PhysRevA.64.052304}, volume = {64}, year = {2001}, }`

- F. Verstraete, K. Audenaert, J. Dehaene, and B. De Moor, “A comparison of the entanglement measures negativity and concurrence,” JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, vol. 34, iss. 47, pp. 10327-10332, 2001.

[Bibtex]`@article{137534, abstract = {In this paper we investigate two different entanglement measures in the case of mixed states of two qubits. We prove that the negativity of a state can never exceed its concurrence and is always larger than root (1 - C)(2) + C-2 - (1 - C), where C is the concurrence of the state. Furthermore, we derive an explicit expression for the states for which the upper or lower bound is satisfied. Finally we show that similar results hold if the relative entropy of entanglement and the entanglement of formation are compared.}, author = {Verstraete, Frank and Audenaert, Koenraad and Dehaene, Jeroen and De Moor, Bart}, issn = {0305-4470}, journal = {JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL}, language = {eng}, number = {47}, pages = {10327--10332}, title = {A comparison of the entanglement measures negativity and concurrence}, url = {http://dx.doi.org/10.1088/0305-4470/34/47/329}, volume = {34}, year = {2001}, }`

- F. Verstraete, J. Dehaene, and B. De Moor, “Local filtering operations on two qubits,” PHYSICAL REVIEW A, vol. 64, iss. 1, p. 4, 2001.

[Bibtex]`@article{137522, abstract = {We consider one single copy of a mixed state of two qubits and investigate how its entanglement changes under local quantum operations and classical communications (LQCC) of the type rho'similar to (A x B)rho (A x B)(dagger). We consider a real matrix parametrization of the set of density matrices and show that these LQCC operations correspond to left and right multiplication by a Lorentz matrix, followed by normalization. A constructive way of bringing this matrix into a normal form is derived. This allows us to calculate explicitly the optimal local filtering operations for concentrating entanglement. Furthermore, we give a complete characterization of the mixed states that can be purified arbitrarily close to a Bell state. Finally, we obtain a new way of calculating the entanglement of formation.}, articleno = {010101}, author = {Verstraete, Frank and Dehaene, J and De Moor, B}, issn = {1050-2947}, journal = {PHYSICAL REVIEW A}, language = {eng}, number = {1}, pages = {4}, title = {Local filtering operations on two qubits}, url = {http://dx.doi.org/10.1103/PhysRevA.64.010101}, volume = {64}, year = {2001}, }`

- K. Audenaert, F. Verstraete, and B. De Moor, “Variational characterizations of separability and entanglement of formation,” PHYSICAL REVIEW A, vol. 64, iss. 5, p. 13, 2001.

[Bibtex]`@article{8594103, abstract = {In this paper we develop a mathematical framework for the characterization of separability and entanglement of formation (EOF) of general bipartite states. These characterizations are variational in nature, meaning that separability and EOF are given in terms of a function that is to be minimized over the manifold of unitary matrices. A major benefit of such a characterization is that it directly leads to a numerical procedure for calculating EOF. We present an efficient minimization algorithm and apply it to the bound entangled 3 x 3 Horodecki states: we show that their EOF is very low and that their distance to the set of separable states is also very small. Within the same variational framework we rephrase the results by Wootters [W. Wootters. Phys. Rev. Lett. 80, 2245 (1998)] on EOF for 2 x 2 states and also present some progress in generalizing these results to higher-dimensional systems.}, articleno = {052304}, author = {Audenaert, K and Verstraete, Frank and De Moor, B}, issn = {1050-2947}, journal = {PHYSICAL REVIEW A}, language = {eng}, number = {5}, pages = {13}, title = {Variational characterizations of separability and entanglement of formation}, url = {http://dx.doi.org/10.1103/PhysRevA.64.052304}, volume = {64}, year = {2001}, }`