Finite-Wavevector Electromagnetic Response of Fractional Quantized Hall States

TL;DR

This paper develops a method to accurately compute the electromagnetic response of fractional quantum Hall states by incorporating mass renormalization effects within a Landau Fermi liquid framework, ensuring compliance with fundamental sum rules.

Contribution

It introduces a novel approach to include mass renormalization in response function calculations for fractional quantum Hall states using Fermi liquid theory.

Findings

Mass renormalization can be effectively incorporated into response calculations.

The approach satisfies Kohn's theorem and the f-sum rules.

Results provide more accurate descriptions of electromagnetic responses.

Abstract

A fractional quantized Hall state with filling fraction $\nu = p/(2mp+1)$ can be modeled as an integer quantized Hall state of transformed fermions, interacting with a Chern-Simons field. The electromagnetic response function for these states at arbitrary frequency and wavevector can be calculated using a semiclassical approximation or the Random Phase Approximation (RPA). However, such calculations do not properly take into account the large effective mass renormalization which is present in the Chern-Simons theory. We show how the mass renormalization can be incorporated in a calculation of the response function within a Landau Fermi liquid theory approach such that Kohn's theorem and the $f$-sum rules are properly satisfied. We present results of such calculations.