Magnetization and dynamically induced finite densities in three-dimensional Chern-Simons QED

TL;DR

This paper investigates how spontaneous magnetization and finite fermion densities arise in three-dimensional Chern-Simons QED, revealing new mechanisms of symmetry breaking and mass generation in finite density vacua.

Contribution

It demonstrates the emergence of spontaneous magnetization and charge condensation in 3D Chern-Simons QED, linking these phenomena to fermion mass and density through Schwinger-Dyson equations.

Findings

Spontaneous magnetization occurs in finite density vacua.

Charge condensation complements fermion-antifermion condensate.

Simultaneous generation of magnetic field and fermion mass at half-filling.

Abstract

In (2+1)-dimensional QED with a Chern-Simons term, we show that spontaneous magnetization occurs in the context of finite density vacua, which are the lowest Landau levels fully or half occupied by fermions. Charge condensation is shown to appear so as to complement the fermion anti-fermion condensate, which breaks the flavor U(2N) symmetry and causes fermion mass generation. The solutions to the Schwinger-Dyson gap equation show that the fermion self-energy contributes to the induction of a finite fermion density and/or fermion mass. The magnetization can be supported by charge condensation for theories with the Chern-Simons coefficient $\kappa=N e^2/2 \pi$, and $\kappa=N e^2/4 \pi$, under the Gauss law constraint. For $\kappa=N e^2/4 \pi$, both the magnetic field and the fermion mass are simultaneously generated in the half-filled ground state, which breaks the U(2N) symmetry as well as the Lorentz symmetry.