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"tensor network"

Glen Evenbly
We propose a new class of tensor network state as a model for the AdS/CFT correspondence and holography. This class is demonstrated to retain key features of the multiscale entanglement renormalization ansatz (MERA), in that they describe quantum states with algebraic correlation functions, have free variational parameters, and are efficiently contractible. Yet, unlike the MERA, they are built according to a uniform tiling of hyperbolic space, without inherent directionality or preferred locations in the holographic bulk, and thus circumvent key arguments made against the MERA as a model for AdS/CFT...
October 6, 2017: Physical Review Letters
Katharine Hyatt, James R Garrison, Bela Bauer
Tensor networks impose a notion of geometry on the entanglement of a quantum system. In some cases, this geometry is found to reproduce key properties of holographic dualities, and subsequently much work has focused on using tensor networks as tractable models for holographic dualities. Conventionally, the structure of the network-and hence the geometry-is largely fixed a priori by the choice of the tensor network ansatz. Here, we evade this restriction and describe an unbiased approach that allows us to extract the appropriate geometry from a given quantum state...
October 6, 2017: Physical Review Letters
Haiyuan Zou, Erhai Zhao, W Vincent Liu
Motivated by the experimental realization of quantum spin models of polar molecule KRb in optical lattices, we analyze the spin 1/2 dipolar Heisenberg model with competing anisotropic, long-range exchange interactions. We show that, by tilting the orientation of dipoles using an external electric field, the dipolar spin system on square lattice comes close to a maximally frustrated region similar, but not identical, to that of the J_{1}-J_{2} model. This provides a simple yet powerful route to potentially realize a quantum spin liquid without the need for a triangular or kagome lattice...
August 4, 2017: Physical Review Letters
Laurens Vanderstraeten, Michaël Mariën, Jutho Haegeman, Norbert Schuch, Julien Vidal, Frank Verstraete
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...
August 18, 2017: Physical Review Letters
Pawel Caputa, Nilay Kundu, Masamichi Miyaji, Tadashi Takayanagi, Kento Watanabe
We introduce a new optimization procedure for Euclidean path integrals, which compute wave functionals in conformal field theories (CFTs). We optimize the background metric in the space on which the path integration is performed. Equivalently, this is interpreted as a position-dependent UV cutoff. For two-dimensional CFT vacua, we find the optimized metric is given by that of a hyperbolic space, and we interpret this as a continuous limit of the conjectured relation between tensor networks and Anti-de Sitter (AdS)/conformal field theory (CFT) correspondence...
August 18, 2017: Physical Review Letters
Adil A Gangat, Te I, Ying-Jer Kao
Directly in the thermodynamic limit, we show how to combine local imaginary and real-time evolution of tensor networks to efficiently and accurately find the nonequilibrium steady states (NESSs) of one-dimensional dissipative quantum lattices governed by a local Lindblad master equation. The imaginary time evolution first bypasses any highly correlated portions of the real-time evolution trajectory by directly converging to the weakly correlated subspace of the NESS, after which, real-time evolution completes the convergence to the NESS with high accuracy...
July 7, 2017: Physical Review Letters
M Bal, M Mariën, J Haegeman, F Verstraete
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)PRLTAO0031-900710.1103/PhysRevLett.115.180405; S. Yang, Z.-C. Gu, and X.-G. Wen, Phys. Rev. Lett. 118, 110504 (2017)PRLTAO0031-900710.1103/PhysRevLett.118.110504], 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...
June 23, 2017: Physical Review Letters
Lauretta R Schwarz, A Alavi, George H Booth
We reformulate the projected imaginary-time evolution of the full configuration interaction quantum Monte Carlo method in terms of a Lagrangian minimization. This naturally leads to the admission of polynomial complex wave function parametrizations, circumventing the exponential scaling of the approach. While previously these functions have traditionally inhabited the domain of variational Monte Carlo approaches, we consider recent developments for the identification of deep-learning neural networks to optimize this Lagrangian, which can be written as a modification of the propagator for the wave function dynamics...
April 28, 2017: Physical Review Letters
H J Liao, Z Y Xie, J Chen, Z Y Liu, H D Xie, R Z Huang, B Normand, T Xiang
The defining problem in frustrated quantum magnetism, the ground state of the nearest-neighbor S=1/2 antiferromagnetic Heisenberg model on the kagome lattice, has defied all theoretical and numerical methods employed to date. We apply the formalism of tensor-network states, specifically the method of projected entangled simplex states, which combines infinite system size with a correct accounting for multipartite entanglement. By studying the ground-state energy, the finite magnetic order appearing at finite tensor bond dimensions, and the effects of a next-nearest-neighbor coupling, we demonstrate that the ground state is a gapless spin liquid...
March 31, 2017: Physical Review Letters
Shuo Yang, Zheng-Cheng Gu, Xiao-Gang Wen
We introduce a tensor renormalization group scheme for coarse graining a two-dimensional tensor network that can be successfully applied to both classical and quantum systems on and off criticality. The key innovation in our scheme is to deform a 2D tensor network into small loops and then optimize the tensors on each loop. In this way, we remove short-range entanglement at each iteration step and significantly improve the accuracy and stability of the renormalization flow. We demonstrate our algorithm in the classical Ising model and a frustrated 2D quantum model...
March 17, 2017: Physical Review Letters
Jun-Sen Xiang, Cong Chen, Wei Li, Xian-Lei Sheng, Na Su, Zhao-Hua Cheng, Qiang Chen, Zi-Yu Chen
In this work, a systematic study of Cu(NO3)2·2.5 H2O (copper nitrate hemipentahydrate, CN), an alternating Heisenberg antiferromagnetic chain model material, is performed with multi-technique approach including thermal tensor network (TTN) simulations, first-principles calculations, as well as magnetization measurements. Employing a cutting-edge TTN method developed in the present work, we verify the couplings J = 5.13 K, α = 0.23(1) and Landé factors g∥= 2.31, g⊥ = 2.14 in CN, with which the magnetothermal properties have been fitted strikingly well...
March 15, 2017: Scientific Reports
Mari Carmen Bañuls, Krzysztof Cichy, J Ignacio Cirac, Karl Jansen, Stefan Kühn
We numerically study the zero temperature phase structure of the multiflavor Schwinger model at nonzero chemical potential. Using matrix product states, we reproduce analytical results for the phase structure for two flavors in the massless case and extend the computation to the massive case, where no analytical predictions are available. Our calculations allow us to locate phase transitions in the mass-chemical potential plane with great precision and provide a concrete example of tensor networks overcoming the sign problem in a lattice gauge theory calculation...
February 17, 2017: Physical Review Letters
Jacob Biamonte
No abstract text is available yet for this article.
March 7, 2017: Proceedings of the National Academy of Sciences of the United States of America
Zhengwei Liu, Alex Wozniakowski, Arthur M Jaffe
We present a 3D topological picture-language for quantum information. Our approach combines charged excitations carried by strings, with topological properties that arise from embedding the strings in the interior of a 3D manifold with boundary. A quon is a composite that acts as a particle. Specifically, a quon is a hemisphere containing a neutral pair of open strings with opposite charge. We interpret multiquons and their transformations in a natural way. We obtain a type of relation, a string-genus "joint relation," involving both a string and the 3D manifold...
March 7, 2017: Proceedings of the National Academy of Sciences of the United States of America
Mingming Li, Shuzhi Sam Ge, Tong Heng Lee
This paper presents a novel content-driven associative memory (CDAM) to associate large-scale color images based on the subjects that represent the images' content. Compared to traditional associative memories, CDAM inherits their tolerance to random noise in images and possesses greater robustness against correlated noise that distorts an image's spatial contextual structure. A three-layer recurrent neural tensor network (RNTN) is designed as the network model of CDAM. Multiple salient objects detection algorithm and partial radial basis function (PRBF) kernel are proposed for subject determination and content-driven association, respectively...
November 29, 2016: IEEE Transactions on Cybernetics
C Krumnow, L Veis, Ö Legeza, J Eisert
Tensor network states and specifically matrix-product states have proven to be a powerful tool for simulating ground states of strongly correlated spin models. Recently, they have also been applied to interacting fermionic problems, specifically in the context of quantum chemistry. A new freedom arising in such nonlocal fermionic systems is the choice of orbitals, it being far from clear what choice of fermionic orbitals to make. In this Letter, we propose a way to overcome this challenge. We suggest a method intertwining the optimization over matrix product states with suitable fermionic Gaussian mode transformations...
November 18, 2016: Physical Review Letters
Tao Liu, Wei Li, Gang Su
Three different tensor network (TN) optimization algorithms are employed to accurately determine the ground state and thermodynamic properties of the spin-3/2 kagome Heisenberg antiferromagnet. We found that the sqrt[3]×sqrt[3] state (i.e., the state with 120^{∘} spin configuration within a unit cell containing 9 sites) is the ground state of this system, and such an ordered state is melted at any finite temperature, thereby clarifying the existing experimental controversies. Three magnetization plateaus (m/m_{s}=1/3,23/27, and 25/27) were obtained, where the 1/3-magnetization plateau has been observed experimentally...
September 2016: Physical Review. E
Robert König, Volkher B Scholz
Matrix product states (MPSs) illustrate the suitability of tensor networks for the description of interacting many-body systems: ground states of gapped 1D systems are approximable by MPSs, as shown by Hastings [M. B. Hastings, J. Stat. Mech. (2007) P08024]. By contrast, whether MPSs and more general tensor networks can accurately reproduce correlations in critical quantum systems or quantum field theories has not been established rigorously. Ample evidence exists: entropic considerations provide restrictions on the form of suitable ansatz states, and numerical studies show that certain tensor networks can indeed approximate the associated correlation functions...
September 16, 2016: Physical Review Letters
Yoshihito Hotta
We propose a tensor-network algorithm for discrete-time stochastic dynamics of a homogeneous system in the thermodynamic limit. We map a d-dimensional nonequilibrium Markov process to a (d+1)-dimensional infinite tensor network by using a higher-order singular-value decomposition. As an application of the algorithm, we compute the nonequilibrium relaxation from a fully magnetized state to equilibrium of the one- and two-dimensional Ising models with periodic boundary conditions. Utilizing the translational invariance of the systems, we analyze the behavior in the thermodynamic limit directly...
June 2016: Physical Review. E
A H Werner, D Jaschke, P Silvi, M Kliesch, T Calarco, J Eisert, S Montangero
Open quantum many-body systems play an important role in quantum optics and condensed matter physics, and capture phenomena like transport, the interplay between Hamiltonian and incoherent dynamics, and topological order generated by dissipation. We introduce a versatile and practical method to numerically simulate one-dimensional open quantum many-body dynamics using tensor networks. It is based on representing mixed quantum states in a locally purified form, which guarantees that positivity is preserved at all times...
June 10, 2016: Physical Review Letters
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