Effect of gauge boson mass on the phase structure of QED${}_3$

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.

arXiv comment10 pages, 2 figures

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