Effect of gauge boson mass on the phase structure of QED$_{3}$

TL;DR

This paper investigates how a finite gauge boson mass influences the phase structure of QED$_{3}$, revealing that increasing gauge boson mass suppresses dynamical chiral symmetry breaking and can restore symmetry.

Contribution

It introduces a study of the impact of gauge boson mass on QED$_{3}$ phase diagram using Dyson-Schwinger equations, linking gauge boson mass to order competition in high-Tc superconductors.

Findings

Gauge boson mass suppresses DCSB

Chiral symmetry is restored above a critical gauge boson mass

Results provide a qualitative picture of order competition in cuprates

Abstract

Dynamical chiral symmetry breaking (DCSB) in QED$_{3}$ with finite gauge boson mass is studied in the framework of the rainbow approximation of Dyson-Schwinger equations. By adopting a simple gauge boson propagator ansatz at finite temperature, we first numerically solve the Dyson-Schwinger equation for the fermion self-energy to determine the chiral phase diagram of QED$_3$ with finite gauge boson mass at finite chemical potential and finite temperature, then we study the effect of the finite gauge mass on the phase diagram of QED$_3$. It is found that the gauge boson mass $m_{a}$ suppresses the occurrence of DCSB. The area of the region in the chiral phase diagram corresponding to DCSB phase decreases as the gauge boson mass $m_{a}$ increases. In particular, chiral symmetry gets restored when $m_{a}$ is above a certain critical value. In this paper, we use DCSB to describe the antiferromagnetic order and use the gauge boson mass to describe the superconducting order. Our results give qualitatively a physical picture on the competition and coexistence between antiferromagnetic order and superconducting orders in high temperature cuprate superconductors.