Composite Fermion Nonlinear Sigma Models

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.