Level fluctuations in quantum systems with multifractal eigenstates

The relationship between universality of level fluctuation laws and multifractality of eigenstates is studied by analyzing energy spectra of tight-binding models of quantum billiards with multifractal eigenstates. We show that level fluctuations in our models are well described by the universal statistical laws such as Poisson statistics for integrable systems and statistics for the Gaussian orthogonal random matrix ensemble as long as the energy levels are located in bandlike spectra, which indicates that level statistics is irrelative to the multifractal properties of eigenstates. Our results are further confirmed by statistical properties of energy spectra in tight-binding models of two-dimensional quasicrystals.