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

The energy density is computed for a U(2) Chern-Simons theory coupled to a nonrelativistic 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 theory’s symmetry, at least in this mean field approximation. For spin-1/2 fermions, we find evidence of ground states with a small non-Abelian charge density, which vanishes as the theory of free fermions is approached. † E-mail: [email protected]