Path Integral for Composite Fermions in the Half-Filled Lowest Landau Level

TL;DR

This paper develops a path integral formulation for composite fermions in the half-filled lowest Landau level, revealing no infrared singularity in the grand-canonical potential at lowest order perturbation theory.

Contribution

It introduces a density-fluctuation-based path integral approach for composite fermions derived from a lattice Hamiltonian, respecting operator order.

Findings

No infrared singularity in the grand-canonical potential at lowest order

Path integral formulation respects operator order

Reveals stability of the system in perturbation theory

Abstract

We consider electrons in two dimensions in a strong magnetic field at half filling of the lowest Landau level using the Chern-Simons approach. Starting from a lattice Hamiltonian for the electrons, we derive a path integral (PI) formulation for the composite fermions (CF) which respects the order of the operators. We use a time lattice with intermediate times in order to have a PI expressed in density fluctuations. This formulation reveals that there is no infrared (IR) singularity in the grand-canonical potential in lowest order perturbation theory.