Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Stable Optimization of Tensor Product Variational State

Andrej Gendiar, Nobuya Maeshima, Tomotoshi Nishino

Published Jan 1, 2008• 21 citations
OpenAlex

Abstract

We consider a variational problem for three-dimensional (3D) classical lattice models. We construct the trial state as a two-dimensional product of local variational weights that contain auxiliary variables. We propose a stable numerical algorithm for the maximization of the variational partition function per layer. Numerical stability and efficiency of the new method is examined through its application to the 3D Ising model. 1

Related papers

Stable Optimization of a Tensor Product Variational State

A. Gendiar, N. Maeshima, T. Nishino

We consider a variational problem for three-dimensional (3D) classical lattice models. We construct the trial state as a two-dimensional product of local variational weights that contain auxiliary variables. We propose a stable numerical algorithm for the maximization of the variational partition function per layer. The numerical stability and efficiency of the new method are examined through its application to the 3D Ising model.

arXiv:cond-mat/0303376•Progress of Theoretical Physics•Oct 1, 2003•50 citations

Stable Optimization of Tensor Product Variational Functions

Andrej Gendiar, Nobuya Maeshima, Tomotoshi Nishino

We consider a variational problem for three-dimensional (3D) classical lattice models, where the trial state is given by a uniform 2D product of local factors. Maximization of the variational partition function draws a self-consistent equation for the local factor. We propose a stable algorithm to solve the equation numerically when the variational function contains many degrees of freedom. Numerical stability and efficiency of the new algorithm is examined through its application to the 3D Ising model. 1

•Mar 19, 2003•0 citations

Two-Dimensional Tensor Product Variational Formulation

T. Nishino, Y. Hieida, K. Okunishi +3 more

We propose a numerical self-consistent method for 3D classical lattice models, which optimizes the variational state written as a two-dimensional product of tensors. The variational partition function is calculated using the corner transfer matrix renormalization group (CTMRG), which is a variant of the density matrix renormalization group (DMRG). The numerical efficiency of the method is exemplified in its application to the 3D Ising model.

arXiv:cond-mat/0011103•Progress of Theoretical Physics•Mar 1, 2001•152 citations

Estimation of the magnetic critical exponent by Tensor Product Variational Approach

Andrej Gendiar, Tomotoshi Nishino, René Derian

A variational problem for three-dimensional (3D) classical lattice models is considered with trial state given by two-dimensional (2D) uniform product of local variational weights. This approach, the tensor product variational approach (TPVA), has been applied to 3D classical models (the Ising and the Potts models). We consider a way of estimating the magnetic critical exponent $β$ for the simple 3D Ising model assuming a functional form of the spontaneous magnetization in the off critical region, where the TPVA provides reliable data.

arXiv:cond-mat/0412192•Dec 8, 2004•2 citations

1Two-Dimensional Tensor Product Variational Formulation

Tomotoshi Nishino, Yasuhiro Hieida, Kouichi Okunishi +2 more

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 matrix renormalization group (CTMRG), which is a variant of the density matrix renormalization group (DMRG). Numerical efficiency of the method is observed via its application to the 3D Ising model. Variational states represented as products of local tensols have been used widely for calculating the ground-state energy in one-dimensional (1D) quantum systems and the free energy in two-dimensional (2D) classical statistical systems. In 1941 Kramers and Wannier calculated a lower bound of the partition function of the 2D

•Jan 1, 2000•59 citations

Tensor Product Variational Formulation for Quantum Systems

Yukinobu Nishio, Nobuya Maeshima, Andrej Gendiar +1 more

We consider a variational problem for the two-dimensional (2D) Heisenberg and XY models, using a trial state which is constructed as a 2D product of local weights. Variational energy is calculated by use of the the corner transfer matrix renormalization group (CTMRG) method, and its upper bound is surveyed. The variational approach is a way of applying the density matrix renormalization group method (DMRG) to infinite size 2D quantum systems.

arXiv:cond-mat/0401115•Jan 8, 2004•42 citations
We consider a variational problem for three-dimensional (3D) classical lattice models. We construct the trial state as a two-dimensional product of local variational weights that contain auxiliary variables. We propose a stable numerical algorithm for the maximization of the variational partition function per layer. Numerical stability and efficiency of the new method is examined through its application to the 3D Ising model. 1
We consider a variational problem for three-dimensional (3D) classical lattice models, where the trial state is given by a uniform 2D product of local factors. Maximization of the variational partition function draws a self-consistent equation for the local factor. We propose a stable algorithm to solve the equation numerically when the variational function contains many degrees of freedom. Numerical stability and efficiency of the new algorithm is examined through its application to the 3D Ising model. 1
A variational problem for three-dimensional (3D) classical lattice models is considered with trial state given by two-dimensional (2D) uniform product of local variational weights. This approach, the tensor product variational approach (TPVA), has been applied to 3D classical models (the Ising and the Potts models). We consider a way of estimating the magnetic critical exponent βββ for the simple 3D Ising model assuming a functional form of the spontaneous magnetization in the off critical region, where the TPVA provides reliable data.
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 matrix renormalization group (CTMRG), which is a variant of the density matrix renormalization group (DMRG). Numerical efficiency of the method is observed via its application to the 3D Ising model. Variational states represented as products of local tensols have been used widely for calculating the ground-state energy in one-dimensional (1D) quantum systems and the free energy in two-dimensional (2D) classical statistical systems. In 1941 Kramers and Wannier calculated a lower bound of the partition function of the 2D