A Criterion for the Critical Number of Fermions and Chiral Symmetry Breaking in Anisotropic QED(2+1)

TL;DR

This paper derives a quantitative criterion for the critical number of fermions in anisotropic QED(2+1), linking velocity anisotropy to chiral symmetry breaking and mass generation, relevant for condensed matter systems.

Contribution

It introduces a new criterion based on photon-fermion coupling analysis to determine the critical fermion number in anisotropic QED(2+1).

Findings

Velocity anisotropy affects the critical fermion number.

A quantum critical point separates gapped and gapless phases.

Relativity restoration occurs in the symmetric phase.

Abstract

By analyzing the strength of a photon-fermion coupling using basic scattering processes we calculate the effect of a velocity anisotropy on the critical number of fermions at which mass is dynamically generated in planar QED. This gives a quantitative criterion which can be used to locate a quantum critical point at which fermions are gapped and confined out of the physical spectrum in a phase diagram of various condensed matter systems. We also discuss the mechanism of relativity restoration within the symmetric, quantum-critical phase of the theory.