Towards a Field Theory of the Plateau Transition

TL;DR

This paper proposes a theoretical framework using the SL(2,C)/SU(2) WZNW model to calculate correlation functions of local densities of states at the plateau transitions in the Integer Quantum Hall effect, providing new analytical tools.

Contribution

It introduces a novel field theory approach for analyzing the local DOS correlations at IQHE plateau transitions, identifying relevant operators and deriving their correlation functions.

Findings

Correlation functions described by the SL(2,C)/SU(2) WZNW model.

Derived differential equations for DOS correlation functions.

OPEs consistent with existing results.

Abstract

We suggest a procedure for calculating correlation functions of the local densities of states (DOS) at the plateau transitions in the Integer Quantum Hall effect (IQHE). We argue that their correlation functions are appropriately described in terms of the SL($2,{\Bbb C}$)/SU(2) WZNW model (at the usual Ka{\v c}--Moody point and with the level $6 \leq k \leq 8$). In this model we have identified the operators corresponding to the local DOS, and derived the partial differential equation determining their correlation functions. The OPEs for powers of the local DOS obtained from this equation are in agreement with available results.