Response Function of the Fractional Quantized Hall State on a Sphere I: Fermion Chern-Simons Theory

TL;DR

This paper models fractional quantum Hall states on a sphere using fermion Chern-Simons theory, calculating their electromagnetic response functions to compare with finite system simulations.

Contribution

It adapts previous response function calculations to spherical geometry, aiding comparison with exact diagonalization results.

Findings

Response functions calculated on a sphere

Facilitates comparison with finite size systems

Supports validation of Chern-Simons theory models

Abstract

Using a well known singular gauge transformation, certain fractional quantized Hall states can be modeled as integer quantized Hall states of transformed fermions interacting with a Chern-Simons field. In previous work we have calculated the electromagnetic response function of these states at arbitrary frequency and wavevector by using the Random Phase Approximation (RPA) in combination with a Landau Fermi Liquid approach. We now adopt these calculations to a spherical geometry in order to facilitate comparison with exact diagonalizations performed on finite size systems.