Non-Abelian Fermionization and Fractional Quantum Hall Transitions

TL;DR

This paper explores dualities in Chern-Simons gauge theories to understand quantum Hall transitions, proposing a non-abelian fermionization approach that offers new theoretical insights into critical exponents and universality.

Contribution

It introduces a non-abelian fermionization framework for fractional quantum Hall transitions, expanding the theoretical landscape beyond abelian gauge field models.

Findings

Large N_f limit does not produce the large exponent ν

Provides a new class of non-abelian gauge theories for quantum Hall transitions

Suggests different parameter space from previous abelian models

Abstract

There has been a recent surge of interest in dualities relating theories of Chern-Simons gauge fields coupled to either bosons or fermions within the condensed matter community, particularly in the context of topological insulators and the half-filled Landau level. Here, we study the application of one such duality to the long-standing problem of quantum Hall inter-plateaux transitions. The key motivating experimental observations are the anomalously large value of the correlation length exponent $\nu \approx 2.3$ and that $\nu$ is observed to be super-universal, i.e., the same in the vicinity of distinct critical points. Duality motivates effective descriptions for a fractional quantum Hall plateau transition involving a Chern-Simons field with $U(N_c)$ gauge group coupled to $N_f = 1$ fermion. We study one class of theories in a controlled limit where $N_f \gg N_c$ and calculate $\nu$ to leading non-trivial order in the absence of disorder. Although these theories do not yield an anomalously large exponent $\nu$ within the large $N_f \gg N_c$ expansion, they do offer a new parameter space of theories that is apparently different from prior works involving abelian Chern-Simons gauge fields.