Universal level-spacing statistics in quasiperiodic tight-binding models

摘要

We study statistical properties of the energy spectra of two-dimensionalquasiperiodic tight-binding models. The multifractal nature of the eigenstatesof these models is corroborated by the scaling of the participation numberswith the systems size. Hence one might have expected `critical' or`intermediate' statistics for the level-spacing distributions as observed atthe metal-insulator transition in the three-dimensional Anderson model ofdisorder. However, our numerical results are in perfect agreement with theuniversal level-spacing distributions of the Gaussian orthogonal random matrixensemble, including the distribution of spacings between second, third, andforth neighbour energy levels.