The integer quantum Hall plateau transition is a current algebra after all

TL;DR

This paper identifies the critical point of the Integer Quantum Hall Effect transition as a non-Abelian current algebra, providing a new conformal field theory description and predicting multifractal exponents.

Contribution

It reveals that the IQHE plateau transition is governed by a level-4 non-Abelian current algebra, connecting the non-linear sigma model to a Wess-Zumino-Witten model with a marginal perturbation.

Findings

Identifies a non-Abelian current algebra at level 4 at criticality.

Predicts multifractal scaling exponents as q(1-q)/4.

Proposes a Wess-Zumino-Witten model as the RG fixed-point theory.

Abstract

The scaling behavior near the transition between plateaus of the Integer Quantum Hall Effect (IQHE) has traditionally been interpreted on the basis of a two-parameter renormalization group (RG) flow conjectured from Pruisken's non-linear sigma model. Yet, the conformal field theory (CFT) describing the critical point remained elusive, and only fragments of a quantitative analytical understanding existed up to now. In the present paper we carry out a detailed analysis of the current-current correlation function for the conductivity tensor, initially in the Chalker-Coddington network model for the IQHE plateau transition and then in its exact reformulation as a supersymmetric vertex model. We develop a heuristic argument for the continuum limit of the non-local conductivity response function at criticality and thus identify a non-Abelian current algebra at level n = 4. Based on precise lattice expressions for the CFT primary fields we predict the multifractal scaling exponents of critical wavefunctions to be q(1-q)/4. The Lagrangian of the RG fixed-point theory for r retarded and r advanced replicas is proposed to be the GL(r|r)_4 Wess-Zumino-Witten model deformed by a truly marginal perturbation. The latter emerges from the non-linear sigma model by a natural scenario of spontaneous symmetry breaking.