Fractional quantum Hall effect in a U(1)×SU(2) gauge field

Abstract

We consider the bosonic fractional quantum Hall (FQH) effect in the presence of a non-Abelian gauge field in addition to the usual Abelian magnetic field. The non-Abelian field breaks the twofold internal state degeneracy, but preserves the Landau level degeneracy. Using exact diagonalization, we find that for moderate non-Abelian field strengths the system's behaviour resembles a single internal state quantum Hall system, while for stronger fields there is a phase transition to either two internal state behaviour or the complete absence of FQH plateaus. Usually the energy gap is reduced by the presence of a non-Abelian field, but some non-Abelian fields appear to slightly increase the gap of the ν=1 and ν=3/2 Read–Rezayi states.