Level Spacing Distribution and Δ3-Statistics of Two Dimensional Disordered Electrons in Strong Magnetic Field

Abstract

The statistical properties of the energy levels of the lowest Landau band are analyzed. The eigenvalues are obtained numerically for a random matrix model that describes a 2D disordered electron system in a strong magnetic field. In order to avoid the problems related to an energy region dependent average level spacing, the original data are unfolded using the ensemble averaged integrated density of states. For the unfolded data, the level spacing distribution and the Δ ₃ -statistics are investigated in order to clarify the level correlations. The statistical properties depend on the energy and the magnitude of the level separation. A continuous change from Poissonian to Gaussian unitary statistics is observed between the edge and the center of the band. For the statistics within a given energy region, a highly non-trivial crossover of symmetries takes place between small and large level separations. Even if the localization length is much larger than the system size the deviations from the Gaussian unitary statistics are not negligible.