Mean Field Theories of Quantum Hall Liquids Justified: Variations on the Greiter Wilczek Theme

TL;DR

This paper introduces a field theoretic approach to Quantum Hall liquids, providing a systematic justification for flux-attachment mean field theories through a Chern-Simons-Maxwell framework, enhancing theoretical understanding.

Contribution

It develops a Chern-Simons-Maxwell theory that makes flux-attachment mean field theory exact in a specific limit, offering a new systematic expansion method.

Findings

Flux-attachment mean field theory is exact in a certain limit

Provides a systematic framework for approximations in Quantum Hall problems

Lays groundwork for future systematic expansions

Abstract

We present a field theoretic variant of the Wilczek - Greiter adiabatic approach to Quantum Hall liquids. Specifically, we define a Chern-Simons-Maxwell theory such that the flux-attachment mean field theory is exact in a certain limit. This permits a systematic way to justify a variety of useful approximate approaches to these problems as constituting the first term in a (still to be developed) systematic expansion about a solvable limit.