An exact expression of the collective excitation energy gap of fractional quantum Hall effect

TL;DR

This paper derives an exact formula for the collective excitation energy gap in the fractional quantum Hall effect, specifically for certain filling factors, using a model of Dirac fermions on a sphere with a magnetic field.

Contribution

It provides the first exact analytical expression for the excitation energy gap at specific fractional filling factors in the quantum Hall effect.

Findings

Exact expression matches numerical computations

Applicable to filling factors =p/(2mpb1 1)

Enhances understanding of quantum Hall excitations

Abstract

We have exactly solved the eigenequation of a two-dimensional Dirac fermion moving on the surface of a sphere under the influence of a radial magnetic field B, and obtained an exact expression of the collective excitation energy gap for the filling factors $\nu=p/(2mp\pm 1)$, m and p are non-zero integers, which is very well agreement with the computing results.