Logarithmic Correlations in Quantum Hall Plateau Transitions

TL;DR

This paper investigates the logarithmic correlations at quantum Hall plateau transitions, providing a non-perturbative construction of disorder-averaged observables and discussing implications for different quantum Hall systems.

Contribution

It introduces a non-perturbative method to construct disorder-averaged observables with logarithmic scaling at quantum critical points using the replica trick and symmetries.

Findings

Logarithmic correlations are shown to describe critical behavior in quantum Hall transitions.

The method applies to spin quantum Hall transition and is compatible with supersymmetry approaches.

Discussion includes generalization to integer quantum Hall plateau transition.

Abstract

The critical behavior of quantum Hall transitions in two-dimensional disordered electronic systems can be described by a class of complicated, non-unitary conformal field theories with logarithmic correlations. The nature and the physical origin of these logarithmic correlation functions remain however mysterious. Using the replica trick and the underlying symmetries of these quantum critical points, we show here how to construct non-perturbatively disorder-averaged observables in terms of Green's functions that scale logarithmically at criticality. In the case of the spin quantum Hall transition, which may occur in disordered superconductors with spin-rotation symmetry and broken time reversal invariance, we argue that our results are compatible with an alternative approach based on supersymmetry. The generalization to the Integer quantum Hall plateau transition is also discussed.