Spin-Allowed Chern-Simons Theory of Fractional Quantum Hall States for Odd and Even Denominator Filling Factors

TL;DR

This paper develops a generalized spin-allowed Chern-Simons theory for fractional quantum Hall states, capturing all odd and even denominator filling factors and analyzing their collective excitations.

Contribution

It introduces a spin-inclusive Chern-Simons framework that unifies descriptions of various polarized fractional quantum Hall states and computes their excitation spectra.

Findings

Reproduces all odd denominator filling factors for different spin polarizations.

Derives electromagnetic response functions and Hall conductivity expressions.

Provides computed spectra of collective excitations satisfying Kohn's theorem.

Abstract

By allowing the spin degrees of freedom, we present a generalized spin allowed $U(1)\times U(1)$ Chern-Simons theory of fractional quantum Hall effects for odd and even denominator filling factors in single layers. This theory is shown to reproduce all possible odd denominator filling factors corresponding to spin-unpolarized, partially polarized, and fully polarized fractional quantum Hall states. Closely following our earlier theory, we derive the formal expressions of electromagnetic polarization tensors and Hall conductivity for the spin-unpolarized and partially polarized fractional quantum Hall states. Finally we report the computed spectra of collective excitations for both the even and odd denominator filling factors for which Kohn's theorem is satisfied.