Application of random matrix theory to quasiperiodic systems

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