Hamiltonian Description of Composite Fermions: Calculation of Gaps

TL;DR

This paper analytically calculates energy gaps for various fractional quantum Hall states using a Hamiltonian Chern-Simons approach, showing good agreement with experiments for soft potentials.

Contribution

It introduces an analytical method based on Hamiltonian Chern-Simons theory to compute gaps in fractional quantum Hall states, including effects of finite sample thickness.

Findings

Good agreement with numerical results

Accurate gap calculations for 1/3, 2/5, 3/7 states

Effective modeling of finite thickness effects

Abstract

We analytically calculate gaps for the 1/3, 2/5, and 3/7 polarized and partially polarized Fractional Quantum Hall states based on the Hamiltonian Chern-Simons theory we have developed. For a class of potentials that are soft at high momenta (due to the finite thickness of the sample) we find good agreement with numerical and experimental results.