Effects of gauge boson mass on chiral and deconfinement phase transitions in QED${}_3$

Abstract

Based on the experimental observation that there is a coexisting region between the antiferromagnetic (AF) and $\text{d}$-wave superconducting ($\text{d}$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 $N_f^c$ decreases as the gauge boson mass $m_a$ increases and there exists a boundary that separates the $N_f^c$-$m_a$ 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.