Composite fermions in the half-filled lowest Landau level: a macroscopic justification

TL;DR

This paper derives an effective Hamiltonian for spinless electrons in the lowest Landau level near half filling, providing a macroscopic justification for composite fermions without eliminating the magnetic field.

Contribution

It introduces a novel approach by projecting onto the LLL before applying a Chern-Simons transformation, offering a new perspective on composite fermions in quantum Hall systems.

Findings

Gauge transformation removes monopole term in interaction

Fermionic commutation relations hold at small wavenumbers

Magnetic field remains after transformation

Abstract

An effective Hamiltonian for spinless electrons in the lowest Landau level (LLL) close to half filling is derived. As opposed to the treatment in standard Chern-Simons theories (CS) we first project to the LLL and only then apply a CS-transformation on the Hamiltonian. The transformed field operators act in the lowest Landau level only {\it and} have fermionic commutation relations for small wavenumbers ignoring gauge field fluctuations. When acting on the Hamiltonian at half filling the {\it gauge transformation removes the monopole term in the interaction and does not eliminate the magnetic field.