Tensor renormalization group study of two-dimensional U(1) lattice gauge theory with a $\theta$ term

TL;DR

This paper uses tensor renormalization group methods to analyze the two-dimensional U(1) lattice gauge theory with a theta term, confirming a first-order phase transition at theta equals pi and matching known exact results.

Contribution

It applies tensor renormalization group techniques to study the phase structure of 2D U(1) lattice gauge theory with a theta term, providing new numerical insights.

Findings

Good agreement of free energy with exact results at finite coupling

Finite gap at theta=pi indicates phase transition

Phase transition at theta=pi is first order

Abstract

We make an analysis of the two-dimensional U(1) lattice gauge theory with a $\theta$ term by using the tensor renormalization group. Our numerical result for the free energy shows good consistency with the exact one at finite coupling constant. The topological charge density generates a finite gap at $\theta=\pi$ toward the thermodynamic limit. In addition finite size scaling analysis of the topological susceptibility up to $V=L\times L=1024\times 1024$ allows us to determine the phase transition at $\theta=\pi$ is the first order.