Composite Fermion Nonlinear Sigma Models

TL;DR

This paper investigates the integer quantum Hall plateau transition using composite fermion mean-field theory, demonstrating the stability of a topological term and the emergence of particle-hole symmetry, with implications for universality.

Contribution

It shows the stability of the topological $ heta = \pi$ term against certain perturbations and reveals emergent particle-hole symmetry in composite fermion theories.

Findings

Topological $ heta = \\pi$ term is stable under specific perturbations.

Emergent particle-hole symmetry in composite fermion models.

Continuous variation of $ heta$ in disordered systems without particle-hole symmetry.

Abstract

We study the integer quantum Hall plateau transition using composite fermion mean-field theory. We show that the topological $\theta = \pi$ term in the associated nonlinear sigma model [P. Kumar et al., Phys. Rev. B 100, 235124 (2019)] is stable against a certain particle-hole symmetry violating perturbation, parameterized by the composite fermion effective mass. This result, which applies to both the Halperin, Lee, and Read and Dirac composite fermion theories, represents an emergent particle-hole symmetry. For a disorder ensemble without particle-hole symmetry, we find that $\theta$ can vary continuously within the diffusive regime. Our results call for further study of the universality of the plateau transition.