Distribution of level curvatures in the lowest Landau level

Abstract

An analysis of the statistics of level curvatures for a system exhibiting the integer quantum Hall effect is presented. The curvatures ${\mathrm{k}}_{\mathrm{n}}$ are calculated numerically and their distribution P(k) is evaluated for energy eigenvalues ${\mathrm{E}}_{\mathrm{n}}$ belonging to insulating as well as to critical states. In the insulating region it is found that P(0)=0 and that P(ln k) depends on the system size, albeit weaker than linearly. There is no clear cut evidence that the distribution is log-normal. The distribution of curvatures corresponding to critical states is scale invariant and appears to be way off the mark set by random matrix theory for the unitary ensemble.