Mean-Field and Perturbation Theory of Vortex-like Composite Fermions

TL;DR

This paper develops a field theory for composite fermions with vortex cores in partially filled Landau levels, establishing a stable mean-field Fermi sea and providing a foundation for understanding vortex-related phenomena in quantum Hall systems.

Contribution

It introduces a novel field theory incorporating vortex cores in composite fermions, with a consistent perturbation approach and stability analysis of the mean-field state.

Findings

Mean-field Fermi sea at half filling is stable.

Low-energy physics matches Chern-Simons fermion theory.

Potential new physics at larger wave vectors.

Abstract

We develop a field theory for a partially filled Landau level based on composite fermions with a finite vortex core, whose mean-field states are exactly those described by well-tested trial wave functions. Despite non-orthogonality of free composite-fermion states and non-Hermiticity of the mean-field Hamiltonian, a consistent perturbation theory is formulated and the mean-field Fermi sea at half filling is shown to be stable. While the low-energy and long-distance physics is the same as in the Chern-Simons fermion theory, new physics is expected to show up for larger wave vectors.