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

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.