Non-minimal Maxwell-Chern-Simons theory and the composite Fermion model

TL;DR

This paper demonstrates that the magnetic field redefinition in the composite fermion model for the fractional quantum Hall effect can be effectively described by a Maxwell-Chern-Simons gauge theory with non-minimal coupling, including a non-relativistic limit of the Dirac equation.

Contribution

It introduces a non-minimal Maxwell-Chern-Simons gauge field framework to model the magnetic field redefinition in the composite fermion approach.

Findings

Effective mean-field description of magnetic field redefinition

Explicit non-relativistic limit of (2+1)D Dirac equation derived

Provides a new theoretical perspective on the fractional quantum Hall effect

Abstract

The magnetic field redefinition in Jain's composite fermion model for the fractional quantum Hall effect is shown to be effectively described by a mean-field approximation of a model containing a Maxwell-Chern-Simons gauge field non-minimally coupled to matter. Also an explicit non-relativistic limit of the non-minimal (2+1)D Dirac equation is derived.