Tensor renormalization group study of (1+1)-dimensional U(1) gauge-Higgs model at $\theta=\pi$ with L\"uscher's admissibility condition

TL;DR

This study uses tensor renormalization group methods to analyze the phase transitions in a (1+1)-dimensional U(1) gauge-Higgs model with a theta term, revealing a first-order transition and a critical endpoint.

Contribution

It introduces a tensor network approach to study the gauge-Higgs model with a theta term, avoiding common simulation issues and identifying phase transition characteristics.

Findings

First-order phase transition at large Higgs mass and θ=π.

Spontaneous breaking of Z2 symmetry at the transition.

Critical behavior consistent with 2D Ising universality class.

Abstract

We investigate the phase structure of the (1+1)-dimensional U(1) gauge-Higgs model with a $\theta$ term, where the U(1) gauge action is constructed with L\"uscher's admissibility condition. Using the tensor renormalization group, both the complex action problem and topological freezing problem in the standard Monte Carlo simulation are avoided. We find the first-order phase transition with sufficiently large Higgs mass at $\theta=\pi$, where the $\mathbb{Z}_2$ charge conjugation symmetry is spontaneously broken. On the other hand, the symmetry is restored with a sufficiently small mass. We determine the critical endpoint as a function of the Higgs mass parameter and show the critical behavior is in the two-dimensional Ising universality class.