Chern-Simons Field Theory of Two-Dimensional Electrons in the Lowest Landau Level

TL;DR

This paper develops a fermion Chern-Simons field theory for two-dimensional electrons in the lowest Landau level, enabling the study of fractional quantum Hall states through a composite fermion framework with an emergent effective mass.

Contribution

It introduces a complete-state-based Chern-Simons theory with a delta-functional constraint, linking composite fermion physics to fractional quantum Hall states with interactions.

Findings

Emergence of an effective mass for low-energy excitations.

Physical interpretation of mass renormalization via lambda.

Mapping fractional to integer quantum Hall states with interactions.

Abstract

We propose a fermion Chern-Simons field theory describing two- dimensional electrons in the lowest Landau level. This theory is constructed with a complete set of states, and the lowest Landau level constraint is enforced through a delta-functional described by an auxiliary field lambda. Unlike the field theory constructed directly with the states in the lowest Landau level, this theory allows one utilizing the physical picture of "composite fermion" to study the fractional quantum Hall states by mapping them onto certain integer quantum Hall states; but unlike it in the unconstrained theory, such a mapping is sensible only when interactions between electrons are present. An "effective mass", which characterizes the scale of low energy excitations in the fractional quantum Hall systems, emerges naturally from our theory. We study a Gaussian effective theory and interpret physically the dressed stationary point equation for lambda as an equation for the "mass renormalization" of composite fermions.