Universal level-spacing statistics in quasiperiodic tight-binding models

Abstract

We studied statistical properties of the energy spectra of two-dimensional quasiperiodic tight-binding models. The multifractal nature of the eigenstates of these models is corroborated by the scaling of the participation numbers with the system size. Hence one might have expected ‘critical’ or ‘intermediate’ statistics for the level-spacing distributions as observed at the metal-insulator transition in the three-dimensional Anderson model of disorder. However, our numerical results are in perfect agreement with the universal level-spacing distributions of the Gaussian orthogonal random matrix ensemble, including the distribution of spacings between second, third, and fourth neighbour energy levels.