Information about the Integer Quantum Hall Transition Extracted from the Autocorrelation Function of Spectral Determinants

TL;DR

This paper uses the autocorrelation function of spectral determinants to analyze the localization and critical behavior of a disordered 2D electron gas near the Integer Quantum Hall transition, revealing size dependence and critical states.

Contribution

It introduces a novel spectral determinant autocorrelation approach to identify localization and critical states in the quantum Hall transition.

Findings

ASD depends trivially on system size for weak magnetic fields, indicating localization.

Nontrivial ASD dependence at Hall conductance 1/2 e^2/h suggests critical wave functions.

Critical behavior persists below a certain disorder strength.

Abstract

The Autocorrelation function of spectral determinants (ASD) is used to probe the sensitivity of a two-dimensional disordered electron gas to the system's size L. For weak magnetic fields ASD is shown to depend only trivially on L, which is a strong indication that all states are localized. From nontrivial dependence of ASD on L for infinite L at a Hall conductance of 1/2 e^2/h we deduce the existence of critical wave functions at this point, as long as the disorder strength does not exceed a critical value.