Coarse-graining renormalization by higher-order singular value decomposition

TL;DR

This paper introduces a new tensor renormalization group method using higher-order singular value decomposition, achieving high accuracy and low computational cost for classical and quantum lattice models in 2D and 3D.

Contribution

The paper presents a novel coarse-graining tensor renormalization technique based on higher-order SVD, improving accuracy and efficiency for lattice models.

Findings

Most accurate 3D Ising model results with up to 16 bond states

Consistent results for 2D quantum transverse Ising model

Effective for both classical and quantum lattice models

Abstract

We propose a novel coarse graining tensor renormalization group method based on the higher-order singular value decomposition. This method provides an accurate but low computational cost technique for studying both classical and quantum lattice models in two- or three-dimensions. We have demonstrated this method using the Ising model on the square and cubic lattices. By keeping up to 16 bond basis states, we obtain by far the most accurate numerical renormalization group results for the 3D Ising model. We have also applied the method to study the ground state as well as finite temperature properties for the two-dimensional quantum transverse Ising model and obtain the results which are consistent with published data.