Global optimization of tensor renormalization group using the corner transfer matrix

TL;DR

This paper introduces a globally optimized tensor network renormalization algorithm using corner transfer matrices, reducing computational cost and improving speed over existing methods in two-dimensional models.

Contribution

The paper presents a novel tensor renormalization algorithm that employs corner transfer matrices for global optimization, eliminating the need for forward-backward iterations and reducing computational complexity.

Findings

The algorithm scales as the sixth power of the bond dimension in 2D.

It outperforms higher-order tensor renormalization methods in speed.

Benchmark tests on the Ising model demonstrate faster solutions.

Abstract

A tensor network renormalization algorithm with global optimization based on the corner transfer matrix is proposed. Since the environment is updated by the corner transfer matrix renormalization group method, the forward-backward iteration is unnecessary, which is a time-consuming part of other methods with global optimization. In addition, a further approximation reducing the order of the computational cost of contraction for the calculation of the coarse-grained tensor is proposed. The computational time of our algorithm in two dimensions scales as the sixth power of the bond dimension while the higher-order tensor renormalization group and the higher-order second renormalization group methods have the seventh power. We perform benchmark calculations in the Ising model on the square lattice and show that the time-to-solution of the proposed algorithm is faster than that of other methods.