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Sep 21, 2013
09/13

by
Norbert Schuch; Frank Verstraete

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One of the central problems in quantum mechanics is to determine the ground state properties of a system of electrons interacting via the Coulomb potential. Since its introduction by Hohenberg, Kohn, and Sham, Density Functional Theory (DFT) has become the most widely used and successful method for simulating systems of interacting electrons, making their original work one of the most cited in physics. In this letter, we show that the field of computational complexity imposes fundamental...

Source: http://arxiv.org/abs/0712.0483v2

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43

Sep 18, 2013
09/13

by
Iztok Pizorn; Frank Verstraete

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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 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...

Source: http://arxiv.org/abs/1102.1401v2

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Sep 21, 2013
09/13

by
Frank Verstraete; Henri Verschelde

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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 the 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.

Source: http://arxiv.org/abs/quant-ph/0203073v3

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69

Sep 23, 2013
09/13

by
Ling Wang; Frank Verstraete

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We propose a novel recursive way of updating the tensors in projected entangled pair states by evolving the tensor in imaginary time evolution on clusters of different sizes. This generalizes the so- called simple update method of Jiang et al. [Phys. Rev. Lett. 101, 090603 (2008)] and the updating schemes in the single layer picture of Pi\v{z}orn et al. [Phys. Rev. A 83, 052321 (2011)]. A finite-size scaling of the observables as a function of the cluster size provides a remarkable improvement...

Source: http://arxiv.org/abs/1110.4362v1

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49

Sep 18, 2013
09/13

by
Frank Verstraete; Henri Verschelde

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One of the most challenging open problems in quantum information theory is to clarify and quantify how entanglement behaves when part of an entangled state is sent through a quantum channel. Of central importance in the description of a quantum channel or completely positive map (CP-map) is the dual state associated to it. The present paper is a collection of well-known, less known and new results on quantum channels, presented in a unified way. We will show how this dual state induces nice...

Source: http://arxiv.org/abs/quant-ph/0202124v2

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85

Sep 17, 2013
09/13

by
Iztok Pizorn; Frank Verstraete

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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 bi-linear 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...

Source: http://arxiv.org/abs/1003.2743v3

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Sep 17, 2013
09/13

by
Kristan Temme; Frank Verstraete

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The concept of stochastic matrix product states is introduced and a natural form for the states is derived. This allows to define the analogue of Schmidt coefficients for steady states of non-equilibrium stochastic processes. We discuss a new measure for correlations which is analogous to the 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 hand...

Source: http://arxiv.org/abs/1003.2545v3

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Sep 18, 2013
09/13

by
Benjamin Toner; Frank Verstraete

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We consider three parties, A, B, and C, each performing one of two local measurements on a shared quantum state of arbitrary dimension. We characterize the trade-off between the nonlocality of the Bell correlations observed by AB and of those observed by AC. This generalizes Tsirelson's bound on the quantum value of the CHSH inequality, the latter being recovered when C is completely uncorrelated with AB. We also discuss the trade-off between Bell violations and local expectation values of...

Source: http://arxiv.org/abs/quant-ph/0611001v1

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Sep 22, 2013
09/13

by
Akimasa Miyake; Frank Verstraete

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We classify multipartite entangled states in the 2 x 2 x n (n >= 4) quantum system, for example the 4-qubit system distributed over 3 parties, under local filtering operations. We show that there exist nine essentially different classes of states, and they give rise to a five-graded partially ordered structure, including the celebrated Greenberger-Horne-Zeilinger (GHZ) and W classes of 3 qubits. In particular, all 2 x 2 x n-states can be deterministically prepared from one maximally...

Source: http://arxiv.org/abs/quant-ph/0307067v3

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6.0

Jun 29, 2018
06/18

by
Valentin Zauner-Stauber; Frank Verstraete

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We demonstrate that the occurrence of symmetry breaking phase transitions together with the emergence of a local order parameter in classical statistical physics is a consequence of the geometrical structure of probability space. To this end we investigate convex sets generated by expectation values of certain observables with respect to all possible probability distributions of classical q-state spins on a two-dimensional lattice, for several values of q. The extreme points of these sets are...

Topics: Statistical Mechanics, Condensed Matter

Source: http://arxiv.org/abs/1607.03492

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Sep 18, 2013
09/13

by
Tobias J. Osborne; Frank Verstraete

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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.

Source: http://arxiv.org/abs/quant-ph/0502176v5

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Sep 22, 2013
09/13

by
Iztok Pizorn; Ling Wang; Frank Verstraete

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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...

Source: http://arxiv.org/abs/1103.2343v1

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55

Sep 20, 2013
09/13

by
Norbert Schuch; Ignacio Cirac; Frank Verstraete

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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. By lifting the requirement of a unique ground state, we obtain a class for which finding the ground state solves an NP-complete problem. Therefore,...

Source: http://arxiv.org/abs/0802.3351v2

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4.0

Jun 29, 2018
06/18

by
Yoju Lee; Frank Verstraete; Andrej Gendiar

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The multistate Potts models on two-dimensional hyperbolic lattices are studied with respect to various boundary effects. The free energy is numerically calculated by 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...

Topics: Statistical Mechanics, Condensed Matter

Source: http://arxiv.org/abs/1606.04009

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47

Sep 22, 2013
09/13

by
Bogdan Pirvu; Jutho Haegeman; Frank Verstraete

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We study a matrix product state (MPS) 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 [1], 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...

Source: http://arxiv.org/abs/1103.2735v1

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Sep 21, 2013
09/13

by
Johannes Wilms; Matthias Troyer; Frank Verstraete

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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 and Renyi mutual information in both Ising and Potts models in 2 dimensions are calculated numerically by combining matrix product states algorithms and Monte...

Source: http://arxiv.org/abs/1011.4421v3

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7.0

Jun 27, 2018
06/18

by
Laurens Vanderstraeten; Frank Verstraete; Jutho Haegeman

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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 non-trivial dispersion relations, spectral weights and two-particle S matrices. Based on this information, we show...

Topics: Strongly Correlated Electrons, Condensed Matter

Source: http://arxiv.org/abs/1506.01008

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62

Sep 20, 2013
09/13

by
Karl Gerd H. Vollbrecht; Frank Verstraete

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We construct new 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 how entanglement-assisted distillation protocols can be converted into non-entanglement-assisted protocols with the same yield.

Source: http://arxiv.org/abs/quant-ph/0404111v2

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110

Sep 19, 2013
09/13

by
Ling Wang; Iztok Pizorn; Frank Verstraete

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It is demonstrated that Monte Carlo sampling can be used to efficiently extract the expectation value of projected entangled pair states with large virtual bond dimension. We use the simple update rule introduced by Xiang et al. to obtain the tensors describing the ground state wavefunction of the antiferromagnetic Heisenberg model and evaluate the finite size energy and staggered magnetization for square lattices with periodic boundary conditions of sizes up to L=16 and virtual bond dimensions...

Source: http://arxiv.org/abs/1010.5450v2

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54

Sep 21, 2013
09/13

by
Martin Schwarz; Kristan Temme; Frank Verstraete

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We present a quantum algorithm to prepare injective 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' parent Hamiltonian.

Source: http://arxiv.org/abs/1104.1410v2

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5.0

Jun 29, 2018
06/18

by
Boye Buyens; Frank Verstraete; Karel Van Acoleyen

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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...

Topics: Quantum Physics, High Energy Physics - Lattice, Condensed Matter, Strongly Correlated Electrons

Source: http://arxiv.org/abs/1606.03385

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71

Sep 17, 2013
09/13

by
Kristan Temme; Michael M. Wolf; Frank Verstraete

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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...

Source: http://arxiv.org/abs/0912.0858v2

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60

Sep 20, 2013
09/13

by
Norbert Schuch; Frank Verstraete; J. Ignacio Cirac

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Superselection rules severly 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), quant-ph/0310124] we showed that this resource can be quantified by a single additional number, the...

Source: http://arxiv.org/abs/quant-ph/0404079v1

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58

Sep 18, 2013
09/13

by
John A. Smolin; Frank Verstraete; Andreas Winter

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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 EPR pair distillation procedure for a given tripartite pure state, and we show that it actually yields EPR and GHZ states; in fact, under a restricted class of protocols, which we call "one-way broadcasting", the GHZ-rate is shown to be optimal. This result implies a capacity theorem for...

Source: http://arxiv.org/abs/quant-ph/0505038v1

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54

Sep 22, 2013
09/13

by
Frank Verstraete; Jeroen Dehaene; Bart De Moor

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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 $\rho'\sim (A\otimes B)\rho(A\otimes B)^{\dagger}$. We consider a real matrix parameterization 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...

Source: http://arxiv.org/abs/quant-ph/0011111v1

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59

Sep 18, 2013
09/13

by
Valentin Murg; Vladimir E. Korepin; Frank Verstraete

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We describe the Algebraic Bethe Ansatz for the spin-1/2 XXX and XXZ Heisenberg chains with open and periodic boundary conditions in terms of tensor networks. These Bethe eigenstates have the structure of Matrix Product States with a conserved number of down-spins. The tensor network formulation suggestes possible extensions of the Algebraic Bethe Ansatz to two dimensions.

Source: http://arxiv.org/abs/1201.5627v1

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129

Jul 19, 2013
07/13

by
Tobias J. Osborne; Jens Eisert; Frank Verstraete

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We show how continuous matrix product states of quantum field theories can be described in terms of the dissipative non-equilibrium dynamics of a lower-dimensional auxiliary boundary field theory. We demonstrate that the spatial correlation functions of the bulk field can be brought into one-to-one correspondence with the temporal statistics of the quantum jumps of the boundary field. This equivalence: (1) illustrates an intimate connection between the theory of continuous quantum measurement...

Source: http://arxiv.org/abs/1005.1268v2

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Jul 20, 2013
07/13

by
Frank Verstraete; Jeroen Dehaene; Bart De Moor

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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 hard, 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...

Source: http://arxiv.org/abs/quant-ph/0107155v1

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65

Sep 18, 2013
09/13

by
Frank Verstraete; Jeroen Dehaene; Bart De Moor

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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 and the 3-tangle), and the optimal local filtering operations maximizing these...

Source: http://arxiv.org/abs/quant-ph/0105090v5

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160

Sep 17, 2013
09/13

by
Frank Verstraete; Jeroen Dehaene; Bart De Moor

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All mixed states of two qubits can be brought into normal form by the action of SLOCC operations of the kind $\rho'=(A\otimes B)\rho(A\otimes B)^\dagger$. These normal forms can be obtained by considering a Lorentz singular value decomposition on a real parameterization 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...

Source: http://arxiv.org/abs/quant-ph/0108043v1

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40

Sep 18, 2013
09/13

by
Valentin Murg; Vladimir E. Korepin; Frank Verstraete

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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, like, for example, correlation functions. In our work,...

Source: http://arxiv.org/abs/1201.5636v2

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6.0

Jun 29, 2018
06/18

by
Laurens Vanderstraeten; Jutho Haegeman; Frank Verstraete; Didier Poilblanc

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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 wavefunctions of the one- and two-particle excitations, and, consequently, the contributions to dynamical correlations. We apply this framework to the (non integrable) frustrated dimerized spin-1/2 chain, a model for generic...

Topics: Condensed Matter, Strongly Correlated Electrons

Source: http://arxiv.org/abs/1603.07665

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49

Jul 20, 2013
07/13

by
Frank Verstraete; J. Ignacio Cirac; Jose I. Latorre

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In recent years, we have witnessed an explosion of experimental tools by which quantum systems can be manipulated in a controlled and coherent way. One of the most important goals now is to build quantum simulators, which would open up the possibility of exciting experiments probing various theories in regimes that are not achievable under normal lab circumstances. Here we present a novel approach to gain detailed control on the quantum simulation of strongly correlated quantum many-body...

Source: http://arxiv.org/abs/0804.1888v1

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Sep 22, 2013
09/13

by
Zheng-Cheng Gu; Frank Verstraete; Xiao-Gang Wen

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The projective construction (the slave-particle approach) has played an very important role in understanding strongly correlated systems, such as the emergence of fermions, anyons, and gauge theory in quantum spin liquids and quantum Hall states. Recently, fermionic Projected Entangled Pair States (fPEPS) have been introduced to effciently represent many-body fermionic states. In this paper, we show that the strongly correlated bosonic/fermionic states obtained both from the projective...

Source: http://arxiv.org/abs/1004.2563v1

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4.0

Jun 29, 2018
06/18

by
Laurens Vanderstraeten; Jutho Haegeman; Philippe Corboz; Frank Verstraete

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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...

Topics: Quantum Physics, Condensed Matter, Strongly Correlated Electrons

Source: http://arxiv.org/abs/1606.09170

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Jun 28, 2018
06/18

by
Laurens Vanderstraeten; Michaël Mariën; Frank Verstraete; Jutho Haegeman

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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...

Topics: Quantum Physics, Strongly Correlated Electrons, Condensed Matter

Source: http://arxiv.org/abs/1507.02151

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5.0

Jun 29, 2018
06/18

by
Damian Draxler; Jutho Haegeman; Frank Verstraete; Matteo Rizzi

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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 states with 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...

Topics: Quantum Physics, Condensed Matter, Quantum Gases

Source: http://arxiv.org/abs/1609.09704

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4.0

Jun 29, 2018
06/18

by
Michaël Mariën; Jutho Haegeman; Paul Fendley; Frank Verstraete

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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...

Topics: Statistical Mechanics, Condensed Matter, Quantum Physics, Strongly Correlated Electrons

Source: http://arxiv.org/abs/1607.05296

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56

Sep 23, 2013
09/13

by
Philippe Corboz; Glen Evenbly; Frank Verstraete; Guifre Vidal

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We propose and test an algorithm to simulate a lattice system of interacting fermions in two spatial dimensions. The approach is an extension of the entanglement renormalization technique [Phys. Rev. Lett. 99, 220405 (2007)] and the related multi-scale entanglement renormalization ansatz. Benchmark calculations for free and interacting fermions on a lattice of $6\times 6$ sites and periodic boundary conditions confirm the validity of this proposal.

Source: http://arxiv.org/abs/0904.4151v2

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Sep 21, 2013
09/13

by
Koenraad M. R. Audenaert; Milan Mosonyi; Frank Verstraete

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In the problem of quantum state discrimination, one has to determine by measurements the state of a quantum system, based on the a priori side information that the true state is one of two given and completely known states, rho or sigma. In general, it is not possible to decide the identity of the true state with certainty, and the optimal measurement strategy depends on whether the two possible errors (mistaking rho for sigma, or the other way around) are treated as of equal importance or not....

Source: http://arxiv.org/abs/1204.0711v4

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4.0

Jun 30, 2018
06/18

by
Jutho Haegeman; Valentin Zauner; Norbert Schuch; Frank Verstraete

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The eigenvalue structure of the quantum transfer matrix is known to encode essential information about the elementary excitations. Here we study transfer matrices of quantum states in a topological phase using the tensor network formalism. We demonstrate that topological quantum order requires a particular type of `symmetry breaking' for the fixed point subspace of the transfer matrix, and relate physical anyon excitations to domain wall excitations at the level of the transfer matrix. A...

Topics: Quantum Physics, Strongly Correlated Electrons, Condensed Matter

Source: http://arxiv.org/abs/1410.5443

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66

Sep 18, 2013
09/13

by
Frank Verstraete; Michael M. Wolf; J. Ignacio Cirac

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We investigate the computational power of creating steady-states of quantum dissipative systems whose evolution is governed by time-independent and local couplings to a memoryless environment. We show that such a model allows for efficient universal quantum computation with the result of the computation encoded in the steady state. Due to the purely dissipative nature of the process, this way of doing quantum computation exhibits some inherent robustness and defies some of the DiVincenzo...

Source: http://arxiv.org/abs/0803.1447v2

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6.0

Jun 28, 2018
06/18

by
Boye Buyens; Jutho Haegeman; Frank Verstraete; Karel Van Acoleyen

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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...

Topics: Quantum Physics, Strongly Correlated Electrons, High Energy Physics - Lattice, Condensed Matter,...

Source: http://arxiv.org/abs/1511.04288

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5.0

Jun 30, 2018
06/18

by
Boye Buyens; Karel Van Acoleyen; Jutho Haegeman; Frank Verstraete

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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...

Topics: High Energy Physics - Lattice, Strongly Correlated Electrons, Condensed Matter

Source: http://arxiv.org/abs/1411.0020

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49

Sep 17, 2013
09/13

by
Frank Verstraete; Koenraad Audenaert; Jeroen Dehaene; Bart De Moor

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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 then $\sqrt{(1-C)^2+C^2}-(1-C)$ 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...

Source: http://arxiv.org/abs/quant-ph/0108021v1

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94

Sep 23, 2013
09/13

by
David Jennings; Jutho Haegeman; Tobias J. Osborne; Frank Verstraete

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We obtain a well-behaved continuum limit of projected entangled pair states (PEPS) that provides an abstract class of quantum field states with natural symmetries. Making use of the recently introduced path integral representation of one-dimensional continuous matrix product states (cMPS) for quantum fields, 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...

Source: http://arxiv.org/abs/1212.3833v1

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4.0

Jun 29, 2018
06/18

by
Nick Bultinck; Dominic J. Williamson; Jutho Haegeman; Frank Verstraete

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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 $\mathbb{Z}_2$ 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 two-fold degeneracy in the entanglement spectrum. Using the fMPS formalism we make explicit the correspondence between the...

Topics: Quantum Physics, Condensed Matter, Strongly Correlated Electrons

Source: http://arxiv.org/abs/1610.07849

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3.0

Jun 30, 2018
06/18

by
You Quan Chong; Valentin Murg; Vladimir Korepin; Frank Verstraete

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We consider a model of strongly correlated electrons in 1D called the t-J model, which was solved by graded algebraic Bethe ansatz. We use it to design graded tensor networks which can be contracted approximately to obtain a Matrix Product State. As a proof of principle, we calculate observables of ground states and excited states of finite lattices up to $18$ lattice sites.

Topics: Strongly Correlated Electrons, Condensed Matter

Source: http://arxiv.org/abs/1411.2839

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45

Sep 22, 2013
09/13

by
J. Ignacio Cirac; Didier Poilblanc; Norbert Schuch; Frank Verstraete

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In many physical scenarios, close relations between the bulk properties of quantum systems and theories associated to 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 (PEPS). 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...

Source: http://arxiv.org/abs/1103.3427v1

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61

Sep 18, 2013
09/13

by
Jutho Haegeman; Tobias J. Osborne; Henri Verschelde; Frank Verstraete

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It is shown how to construct renormalization group 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 wavefunctions arising from this RG flow are translation invariant and exhibit an entropy-area law. We illustrate the construction for a free non-relativistic boson model, and argue that the full power of the...

Source: http://arxiv.org/abs/1102.5524v2