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

TL;DR

This paper investigates how non-Abelian gauge fields influence the bosonic fractional quantum Hall effect, revealing phase transitions and effects on energy gaps, with potential implications for understanding topological states in complex gauge environments.

Contribution

It introduces the study of bosonic fractional quantum Hall states under combined Abelian and non-Abelian gauge fields, highlighting phase transitions and gap modifications.

Findings

Moderate non-Abelian fields mimic single internal state behavior.

Strong non-Abelian fields induce phase transitions or destroy fractional quantum Hall states.

Some non-Abelian fields slightly increase energy gaps for specific states.

Abstract

We consider the bosonic fractional quantum Hall 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 fractional quantum Hall 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 $\nu=1$ and $\nu=3/2$ Read-Rezayi states.