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"tensor network"

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
Shi-Ju Ran
In this work, a simple and fundamental numeric scheme dubbed as ab initio optimization principle (AOP) is proposed for the ground states of translational invariant strongly correlated quantum lattice models. The idea is to transform a nondeterministic-polynomial-hard ground-state simulation with infinite degrees of freedom into a single optimization problem of a local function with finite number of physical and ancillary degrees of freedom. This work contributes mainly in the following aspects: (1) AOP provides a simple and efficient scheme to simulate the ground state by solving a local optimization problem...
May 2016: Physical Review. E
G Evenbly, G Vidal
Consider the partition function of a classical system in two spatial dimensions, or the Euclidean path integral of a quantum system in two space-time dimensions, both on a lattice. We show that the tensor network renormalization algorithm [G. Evenbly and G. Vidal Phys. Rev. Lett. 115, 180405 (2015)] can be used to implement local scale transformations on these objects, namely, a lattice version of conformal maps. Specifically, we explain how to implement the lattice equivalent of the logarithmic conformal map that transforms the Euclidean plane into a cylinder...
January 29, 2016: Physical Review Letters
G Evenbly, G Vidal
We show how to build a multiscale entanglement renormalization ansatz (MERA) representation of the ground state of a many-body Hamiltonian H by applying the recently proposed tensor network renormalization [G. Evenbly and G. Vidal, Phys. Rev. Lett. 115, 180405 (2015)] to the Euclidean time evolution operator e(-βH) for infinite β. This approach bypasses the costly energy minimization of previous MERA algorithms and, when applied to finite inverse temperature β, produces a MERA representation of a thermal Gibbs state...
November 13, 2015: Physical Review Letters
G Evenbly, G Vidal
We introduce a coarse-graining transformation for tensor networks that can be applied to study both the partition function of a classical statistical system and the Euclidean path integral of a quantum many-body system. The scheme is based upon the insertion of optimized unitary and isometric tensors (disentanglers and isometries) into the tensor network and has, as its key feature, the ability to remove short-range entanglement or correlations at each coarse-graining step. Removal of short-range entanglement results in scale invariance being explicitly recovered at criticality...
October 30, 2015: Physical Review Letters
J Haegeman, V Zauner, N Schuch, F Verstraete
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...
2015: Nature Communications
Arne L Grimsmo
A theory of time-delayed coherent quantum feedback is developed. More specifically, we consider a quantum system coupled to a bosonic reservoir creating a unidirectional feedback loop. It is shown that the dynamics can be mapped onto a fictitious series of cascaded quantum systems, where the system is driven by past versions of itself. The derivation of this model relies on a tensor network representation of the system-reservoir time propagator. For concreteness, this general theory is applied to a driven two-level atom scattering into a coherent feedback loop...
August 7, 2015: Physical Review Letters
Hyungwon Kim, Mari Carmen Bañuls, J Ignacio Cirac, Matthew B Hastings, David A Huse
We numerically construct slowly relaxing local operators in a nonintegrable spin-1/2 chain. Restricting the support of the operator to M consecutive spins along the chain, we exhaustively search for the operator that minimizes the Frobenius norm of the commutator with the Hamiltonian. We first show that the Frobenius norm bounds the time scale of relaxation of the operator at high temperatures. We find operators with significantly slower relaxation than the slowest simple "hydrodynamic" mode due to energy diffusion...
July 2015: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Sazi Li, Wei Li, Ziyu Chen
In this work, we investigate the classical loop models doped with monomers and dimers on a square lattice, whose partition function can be expressed as a tensor network (TN). In the thermodynamic limit, we use the boundary matrix product state technique to contract the partition function TN, and determine the thermodynamic properties with high accuracy. In this monomer-dimer-loop model, we find a second-order phase transition between a trivial monomer-condensation and a loop-condensation (LC) phase, which cannot be distinguished by any local order parameter, while nevertheless the two phases have distinct topological properties...
June 2015: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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