Mean Field Theory for Fermion-based U(2) Anyons

TL;DR

This paper uses mean-field theory to analyze the energy density and symmetry properties of U(2) Chern-Simons theories coupled to non-relativistic fermions, revealing different behaviors for spinless and spin-1/2 cases.

Contribution

It provides a mean-field analysis of non-Abelian anyons in U(2) Chern-Simons theories, highlighting the conditions for symmetry breaking and the behavior of non-Abelian charge density.

Findings

Energy density is independent of coupling constants for spinless fermions.

No spontaneous SU(2) symmetry breaking in the spinless case.

Spin-1/2 fermions exhibit small non-Abelian charge density states.

Abstract

The energy density is computed for a U(2) Chern-Simons theory coupled to a non-relativistic fermion field (a theory of ``non-Abelian anyons'') under the assumptions of uniform charge and matter density. When the matter field is a spinless fermion, we find that this energy is independent of the two Chern-Simons coupling constants and is minimized when the non-Abelian charge density is zero. This suggests that there is no spontaneous breaking of the SU(2) subgroup of the symmetry, at least in this mean-field approximation. For spin-1/2 fermions, we find self-consistent mean-field states with a small non-Abelian charge density, which vanishes as the theory of free fermions is approached.