The Fermion Chern-Simons Gauge Theory of Fractional Quantum Hall Effect for Electromagnetic Polarization Tensor

TL;DR

This paper reformulates the fermion Chern-Simons gauge theory for the fractional quantum Hall effect to derive a self-consistent electromagnetic polarization tensor based on the residual magnetic field experienced by composite fermions, improving upon earlier models.

Contribution

It introduces a new formulation that avoids certain assumptions, providing a self-consistent way to calculate the electromagnetic polarization tensor in fractional quantum Hall systems.

Findings

Reproduces the Hall conductance accurately.

Shows the polarization tensor depends on the residual magnetic field.

Maintains a self-consistent composite fermion picture.

Abstract

Unlike an earlier theory, by avoiding both the electromagnetic gauge field shift and the assumption of the zero average of electromagnetic field fluctuation the fermion Chern-Simons gauge theory is reformulated to obtain mean field solutions and a self-consistent expression of the electromagnetic polarization tensor in terms of the composite fermion picture for the systems of fractional quantum Hall effect. Thus the newly derived electromagnetic polarization tensor is shown to depend on the residual (effective) magnetic field `seen' by composite fermions rather than the statistical field, which differs from the earlier theory. The present theory reproduces the Hall conductance of fractional quantum Hall effect. The self-consistent picture of the composite fermion is maintained in all of our derivations: both the mean field solutions and the electromagnetic polarization tensor are described by the residual magnetic field seen by the composite fermions.