Level-Spacing Distributions of Planar Quasiperiodic Tight-Binding Models

摘要

We study the statistical properties of energy spectra of two-dimensionalquasiperiodic tight-binding models. We demonstrate that the nearest-neighborlevel spacing distributions of these non-random systems are well described byrandom matrix theory. Properly taking into account the symmetries of modelsdefined on various finite approximants of quasiperiodic tilings, we find thatthe underlying universal level-spacing distribution is given by theWigner-Dyson distribution of the Gaussian orthogonal random matrix ensemble.Our data allow us to see the differences between the Wigner surmise and theexact level-spacing distribution. In particular, our result differs from thecritical level-spacing distribution computed at the metal-insulator transitionin the three-dimensional Anderson model of disorder.