Lowest-Landau-level theory of the quantum Hall effect: the Fermi-liquid-like state

TL;DR

This paper develops a lowest Landau level theory for a Fermi-liquid-like state of charged bosons at filling factor one, revealing a gauge theory with unique properties and similarities to existing models.

Contribution

It introduces a gauge-theoretic approach using fermions with constraints, leading to a novel description of the Fermi-liquid-like state in the lowest Landau level.

Findings

The system is compressible with Fermi-liquid characteristics.

Fermions are effectively neutral but possess a dipole moment.

The response functions are explicitly calculated.

Abstract

A theory for a Fermi-liquid-like state in a system of charged bosons at filling factor one is developed, working in the lowest Landau level. The approach is based on a representation of the problem as fermions with a system of constraints, introduced by Pasquier and Haldane (unpublished). This makes the system a gauge theory with gauge algebra W_infty. The low-energy theory is analyzed based on Hartree-Fock and a corresponding conserving approximation. This is shown to be equivalent to introducing a gauge field, which at long wavelengths gives an infinite-coupling U(1) gauge theory, without a Chern-Simons term. The system is compressible, and the Fermi-liquid properties are similar, but not identical, to those in the previous U(1) Chern-Simons fermion theory. The fermions in the theory are effectively neutral but carry a dipole moment. The density-density response, longitudinal conductivity, and the current density are considered explicitly.