Novel Scaling Relation of the Energy Spacing Distribution in Quantum-Hall Systems

TL;DR

This paper uncovers a new scale-invariant relation in the energy spacing distribution of disordered quantum Hall systems, revealing how disorder correlations influence universal behavior and length scales.

Contribution

It introduces a novel scaling relation based on Rényi-entropy differences in energy spacing distributions, highlighting the effects of disorder correlations and Landau-band variations.

Findings

Discovered a scale-invariant relation in $P(s)$ related to Rényi-entropy differences.

Identified a large, irrelevant length scale in uncorrelated disorder cases.

Showed that disorder correlations eliminate the large length scale, restoring universality.

Abstract

The shape analysis of the energy spacing distribution $P(s)$ obtained from numerical simulation of two dimensional disordered electron systems subject to strong magnetic fields is performed. In the present work we reanalyze the data obtained in a previous publication. Special moments of the $P(s)$ function related to R\'enyi-entropy differences show a novel scale invariant relation that is attributed to the presence of one-parameter scaling. This relation seems to show both deviations and universality depending on which Landau-band is considered and whether the disorder is correlated or uncorrelated. Furthermore, our analysis shows the existence of an huge, however, irrelevant length scale in the case of the second lowest Landau-band and no disorder correlations that completely disappears with the introduction of disorder correlations on the range of one magnetic length.