Stable Optimization of a Tensor Product Variational State

TL;DR

This paper introduces a stable and efficient numerical method for optimizing a variational state in 3D classical lattice models, demonstrated on the 3D Ising model, improving computational stability and accuracy.

Contribution

It presents a novel stable algorithm for maximizing the variational partition function in 3D lattice models using a tensor product variational state.

Findings

The method achieves numerical stability in 3D Ising model calculations.

It improves efficiency over previous optimization techniques.

The approach effectively handles auxiliary variables in the variational state.

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. The numerical stability and efficiency of the new method are examined through its application to the 3D Ising model.