Related papers: Tensor Network Based Finite-Size Scaling for Two-D…
We propose the use of Monte Carlo histogram reweighting to extrapolate predictions of machine learning methods. In our approach, we treat the output from a convolutional neural network as an observable in a statistical system, enabling its…
In this paper, we propose a parallel computing method for the Higher Order Tensor Renormalization Group (HOTRG) applied to a $d$-dimensional $( d \geq 2 )$ simple lattice model. Sequential computation of the HOTRG requires $O ( \chi^{4 d -…
Recently, the tensor network description with bond weights on its edges has been proposed as a novel improvement for the tensor renormalization group algorithm. The bond weight is controlled by a single hyperparameter, whose optimal value…
We study two-dimensional ferromagnetic Ising model on a series of regular lattices, which are represented as the tessellation of polygons with p>=5 sides, such as pentagons (p=5), hexagons (p=6), etc. Such lattices are on hyperbolic planes,…
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…
Aimed at a more realistic classical description of natural quantum systems, we present a two-dimensional tensor network algorithm to study finite temperature properties of frustrated model quantum systems and real quantum materials. For…
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…
We have proposed a novel numerical method to calculate accurately the physical quantities of the ground state with the tensor-network wave function in two dimensions. We determine the tensor network wavefunction by a projection approach…
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…
We propose a second renormalization group (SRG) in the triad representation of tensor networks. The SRG method improves two parts of the triad tensor renormalization group, which are the decomposition of intermediate tensors and the…
In the context of tensor network states, we for the first time reformulate the corner transfer matrix renormalization group (CTMRG) method into a variational bilevel optimization algorithm. The solution of the optimization problem…
The new algorithm of the finite lattice method is applied to generate the high-temperature expansion series of the simple cubic Ising model to $\beta^{50}$ for the free energy, to $\beta^{32}$ for the magnetic susceptibility and to…
The Ising-like anisotropy parameter $\delta$ in the Kondo necklace model is analyzed using the bond-operator method at zero and finite temperatures for arbitrary $d$ dimensions. A decoupling scheme on the double time Green's functions is…
Tensor network methods are powerful and efficient tools to study the properties and dynamics of statistical and quantum systems, in particular in one and two dimensions. In recent years, these methods were applied to lattice gauge theories,…
The tensor renormalization group attracts great attention as a new numerical method that is free of the sign problem. In addition to this striking feature, it also has an attractive aspect as a coarse-graining of space-time; the…
We study the ferromagnetic transverse-field Ising model with quenched disorder at $T = 0$ in one and two dimensions by means of stochastic series expansion quantum Monte Carlo simulations using a rigorous zero-temperature scheme. Using a…
Recent developments in analog quantum simulators based on cold atoms and trapped ions call for cross-validating the accuracy of quantum-simulation experiments with use of quantitative numerical methods; however, it is particularly…
We propose a numerical self-consistent method for 3D classical lattice models, which optimizes the variational state written as two-dimensional product of tensors. The variational partition function is calculated by the corner transfer…
The corrections to finite-size scaling in the critical two-point correlation function G(r) of 2D Ising model on a square lattice have been studied numerically by means of exact transfer-matrix algorithms. The systems of square geometry with…
Machine learning is becoming widely used in condensed matter physics. Inspired by the concept of image super-resolution, we propose a method to increase the size of lattice spin configurations using deep convolutional neural networks.…