Tensor renormalization group study of the three-dimensional SU(2) and SU(3) gauge theories with the reduced tensor network formulation

TL;DR

This paper applies tensor renormalization group methods to three-dimensional non-Abelian SU(2) and SU(3) gauge theories using a novel 'armillary sphere' tensor formulation, successfully identifying deconfinement transitions.

Contribution

It introduces a reduced tensor network formulation based on the 'armillary sphere' that simplifies the tensor structure by tracing out matrix indices, enabling efficient simulations of non-Abelian gauge theories.

Findings

Accurately computes average plaquette and Polyakov loop susceptibility.

Identifies deconfinement transition points for SU(2) and SU(3).

Results for SU(2) are consistent with previous Monte Carlo studies.

Abstract

We perform a tensor renormalization group simulation of non-Abelian gauge theory in three dimensions using a formulation based on the `armillary sphere.' In this formulation, matrix indices are completely traced out, eliminating the degeneracy in the singular value spectrum of the initial tensor. We demonstrate the usefulness of this technique by computing the average plaquette at zero temperature and the Polyakov loop susceptibility at finite temperatures for 2+1D SU(2) and SU(3) gauge theories. The deconfinement transition is identified for both gauge groups, with the SU(2) case being consistent with previous Monte Carlo results.