Effects of gauge boson mass on chiral and deconfinement phase transitions in QED$_{3}$

TL;DR

This study investigates how the mass of gauge bosons influences chiral symmetry restoration and deconfinement phase transitions in QED3, revealing second-order transitions and a boundary in the parameter space that separates different phases.

Contribution

It provides a unified analysis of gauge boson mass effects on phase transitions in QED3 using Dyson-Schwinger equations, highlighting the relationship between fermion flavor number and phase boundaries.

Findings

Chiral symmetry restoration transition is second-order.

Chiral symmetry restoration and deconfinement transitions coincide.

Critical fermion flavor number decreases with increasing gauge boson mass.

Abstract

Based on the experimental observation that there is a coexisting region between the antiferromagnetic (AF) and $\textit{d}$-wave superconducting ($\textit{d}$SC) phases, the influences of gauge boson mass $m_{a}$ on chiral symmetry restoration and deconfinement phase transitions in QED$_{3}$ are investigated simultaneously within a unified framework, i.e., Dyson-Schwinger equations. The results show that the chiral symmetry restoration phase transition in the presence of the gauge boson mass $m_{a}$ is a typical second-order phase transition; the chiral symmetry restoration and deconfinement phase transitions are coincident; the critical number of fermion flavors $N^{c}_{f}$ decreases as the gauge boson mass $m_{a}$ increases and there exists a boundary that separates the $N^{c}_{f}$-$m_{a}$ plane into chiral symmetry breaking/confinement region for ($N_{f}^{c}$, $m_{a}$) below the boundary and chiral symmetry restoration/deconfinement region for ($N_{f}^{c}$, $m_{a}$) above it.