Related papers: Self-Consistent Tensor Product Variational Approxi…

The Density Matrix Renormalization Group (DMRG) method with periodic boundary conditions is introduced for two dimensional classical spin models. It is shown that this method is more suitable for derivation of the properties of infinite 2D…

We show that the matrix (or more generally tensor) product states in a finite translation invariant system can be accurately constructed from the same set of local matrices (or tensors) that are determined from an infinite lattice system in…

We propose a scheme to perform tensor network based finite-size scaling analysis for two-dimensional classical models. In the tensor network representation of the partition function, we use higher-order tensor renormalization group (HOTRG)…

The classical two-dimensional anisotropic triangular nearest-neighbor Ising (ATNNI) model is studied by the density matrix renormalization group (DMRG) technique when periodic boundary conditions are imposed. Applying the finite-size…

We show that the formalism of tensor-network states, such as the matrix product states (MPS), can be used as a basis for variational quantum Monte Carlo simulations. Using a stochastic optimization method, we demonstrate the potential of…

The Density Matrix Renormalization Group (DMRG) has become a powerful numerical method that can be applied to low-dimensional strongly correlated fermionic and bosonic systems. It allows for a very precise calculation of static, dynamical…

Tensor network methods have progressed from variational techniques based on matrix-product states able to compute properties of one-dimensional condensed-matter lattice models into methods rooted in more elaborate states such as projected…

We report a physical background of the wave function prediction in the infinite system density matrix renormalization group (DMRG) method, from the view point of two-dimensional vertex model, a typical lattice model in statistical…

We propose a modification of the non-perturbative renormalization-group (NPRG) which applies to lattice models. Contrary to the usual NPRG approach where the initial condition of the RG flow is the mean-field solution, the lattice NPRG uses…

We develop a tensor network technique that can solve universal reversible classical computational problems, formulated as vertex models on a square lattice [Nat. Commun. 8, 15303 (2017)]. By encoding the truth table of each vertex…

Motivated by the growing interest in self-correcting quantum memories, we study the feasibility of self-correction in classical lattice systems composed of bounded degrees of freedom with local interactions. We argue that self-correction,…

We study the $q$-state Potts models on a cubic lattice in the thermodynamic limit using tensor renormalization group transformations with the triad approximation. By computing the thermodynamic potentials, we locate the first-order phase…

Hybrid classical-quantum algorithms aim at variationally solving optimisation problems, using a feedback loop between a classical computer and a quantum co-processor, while benefitting from quantum resources. Here we present experiments…

Using tensor network states to unravel the physics of quantum spin liquids in minimal, yet generic microscopic spin or electronic models remains notoriously challenging. A prominent open question concerns the nature of the insulating ground…

Tensor networks (TNs) have become one of the most essential building blocks for various fields of theoretical physics such as condensed matter theory, statistical mechanics, quantum information, and quantum gravity. This review provides a…

We have discussed the tensor-network representation of classical statistical or interacting quantum lattice models, and given a comprehensive introduction to the numerical methods we recently proposed for studying the tensor-network…

The development of tensor renormalization group (TRG) algorithm in higher dimensions is an important and urgent task, as the TRG is expected to provide a way to overcome the sign problem in lattice quantum chromodynamics (QCD) calculations…

Tensor renormalization group, originally devised as a numerical technique, is emerging as a rigorous analytical framework for studying lattice models in statistical physics. Here we introduce a new renormalization map - the 2x1 map - which…

The tensor renormalization group is a promising numerical method used to study lattice statistical field theories. However, this approach is computationally expensive in 2+1 and 3+1 dimensions. Here we use tensor renormalization group…

The self-consistent Gaussian approximation (SCGA) for classical spin systems described by a completely anisotropic D-component vector model is proposed, which takes into account fluctuations of the molecular field and thus is a next step…