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

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.

arXiv commentRevtex, 11 pages, no figures