Level statistics in the quantum Hall regime

TL;DR

This paper studies the statistical properties of energy levels in the quantum Hall regime, focusing on level spacing distribution and correlation length scaling, revealing discrepancies with some predictions but aligning with others.

Contribution

It provides new numerical analysis of level statistics in the quantum Hall regime, especially regarding the scaling exponent of the correlation length.

Findings

Level spacing distribution disagrees with recent analytical predictions.

The scaling exponent $ u$ agrees with theoretical and experimental results.

The Mehta quantity $I_0$ effectively derives the correlation length exponent.

Abstract

The statistical properties of energy eigenvalues in the critical regime of the lowest Landau band are investigated. The nearest neighbour level spacing distribution $P(s)$ and the Mehta quantity $I_0$, from which the scaling exponent $\nu$ of the correlation length can be derived, are calculated. While $P(s)$ disagrees with recent analytical predictions, $\nu$ is found to be in agreement with theoretical and experimental results.