Non-Fermi liquid behavior due to U(1) gauge field in two dimensions

TL;DR

This paper investigates the damping rate of massless Dirac fermions coupled to a U(1) gauge field in 2D, revealing non-Fermi liquid behavior when the Maxwell term is included, with divergence issues resolved.

Contribution

It demonstrates how including the Maxwell term in (2+1)D quantum electrodynamics leads to finite fermion damping rates and non-Fermi liquid behavior.

Findings

Fermion damping rate diverges without Maxwell term.

Including Maxwell term resolves divergence issues.

Fermion damping rate scales as max(√ω, √T).

Abstract

We study the damping rate of massless Dirac fermions due to the U(1) gauge field in (2+1)-dimensional quantum electrodynamics. In the absence of a Maxwell term for the gauge field, the fermion damping rate $\mathrm{Im}\Sigma(\omega,T)$ is found to diverge in both perturbative and self-consistent results. In the presence of a Maxwell term, there is still divergence in the perturbative results for $\mathrm{Im}\Sigma(\omega,T)$. Once the Maxwell term is included into the self-consistent equations for fermion self-energy and vacuum polarization functions, the fermion damping rate is free of divergence and exhibits non-Fermi liquid behavior: $\mathrm{Im}\Sigma(\omega,T) \propto \mathrm{max}(\sqrt{\omega},\sqrt{T})$.