Level-Spacing Distributions of Planar Quasiperiodic Tight-Binding Models

Abstract

We study statistical properties of energy spectra of two-dimensional quasiperiodic tight-binding models. Taking into account the symmetries of models defined on various finite approximants of quasiperiodic tilings, we find that the underlying universal level-spacing distribution is given by the Gaussian orthogonal random matrix ensemble. Our data allow us to see the difference to the Wigner surmise. In particular, our result differs from the critical level-spacing distribution observed at the metal-insulator transition in the three-dimensional Anderson model of disorder.