Gauge Invariance and the Critical Properties of Quantum Hall Plateaux Transitions

TL;DR

This paper introduces a gauge-invariant model with SL(2,Z) symmetry to describe quantum Hall plateau transitions, predicting a correlation length exponent that matches experimental data.

Contribution

It proposes a novel gauge-invariant model incorporating impurities to accurately describe quantum Hall transitions and their critical properties.

Findings

Correlation length exponent of 20/9 matches experiments

Model exhibits SL(2,Z) symmetry due to gauge invariance

Describes transitions between quantum Hall plateaux

Abstract

A model consisting of a single massless scalar field with a topological coupling to a pure gauge field is defined and studied. It possesses an SL(2,Z) symmetry as a consequence of the gauge invariance. We propose that by adding impurities the model can be used to describe transitions between Quantum Hall plateaux. This leads to a correlation length exponent of 20/9, in excellent agreement with the most recent experimental measurements.