On the interaction energy of 2D electron FQHE systems within the Chern-Simons approach

TL;DR

This paper investigates the interaction energy in 2D electron systems exhibiting fractional quantum Hall effect using the Chern-Simons composite fermion approach, comparing RPA results with exact diagonalization and highlighting discrepancies.

Contribution

It provides a comparison of RPA calculations with exact results for fractional quantum Hall states, revealing limitations of the Chern-Simons approach in this context.

Findings

RPA results poorly match exact diagonalization data

Discrepancies suggest need for alternative theoretical methods

Analysis focused on specific filling factors like 1/3, 1/5, 2/3, 2/5, 3/7

Abstract

The interaction energy of the two-dimensional electron system in the region of fractional quantum Hall effect is considered within the Chern-Simons composite fermion approach. In the limit when Coulomb interaction is very small comparing to the cyclotron energy the RPA results are obtained for the fillings $\nu=1/3, 1/5, 2/3, 2/5, 3/7$ and compared with the exact diagonalization results for small systems (extrapolated for infinite systems). They show very poor agreement suggesting the need for looking for alternative approaches.