Tensor renormalization group study of (3+1)-dimensional $Z_2$ gauge-Higgs model at finite density

TL;DR

This paper applies the tensor renormalization group method to study the phase transitions of the (3+1)-dimensional $Z_2$ gauge-Higgs model at finite density, providing new insights into its critical endpoints and demonstrating the method's potential for four-dimensional lattice gauge theories.

Contribution

First application of tensor renormalization group to a 4D lattice gauge theory, analyzing critical endpoints at finite density and comparing results with previous methods.

Findings

In (2+1)D, results agree with Monte Carlo estimates.

In (3+1)D, critical endpoint location differs from mean-field and Monte Carlo estimates.

Demonstrates tensor RG's potential for studying finite density QCD.

Abstract

We investigate the critical endpoints of the (3+1)-dimensional $Z_2$ gauge-Higgs model at finite density together with the (2+1)-dimensional one at zero density as a benchmark using the tensor renormalization group method. We focus on the phase transition between the Higgs phase and the confinement phase at finite chemical potential along the critical end line. In the (2+1)-dimensional model, the resulting endpoint is consistent with a recent numerical estimate by the Monte Carlo simulation. In the (3+1)-dimensional case, however, the location of the critical endpoint shows disagreement with the known estimates by the mean-field approximation and the Monte Carlo studies. This is the first application of the tensor renormalization group method to a four-dimensional lattice gauge theory and a key stepping stone toward the future investigation of the phase structure of the finite density QCD.