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Universal level-spacing statistics in quasiperiodic tight-binding models

Uwe Grimm·Rudolf A. Roemer·Michael Schreiber·Jian-Xin Zhong
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Abstract

We study statistical properties of the energy spectra of two-dimensional quasiperiodic tight-binding models. The multifractal nature of the eigenstates of these models is corroborated by the scaling of the participation numbers with the systems size. Hence one might have expected `critical' or `intermediate' statistics for the level-spacing distributions as observed at the metal-insulator transition in the three-dimensional Anderson model of disorder. However, our numerical results are in perfect agreement with the universal level-spacing distributions of the Gaussian orthogonal random matrix ensemble, including the distribution of spacings between second, third, and forth neighbour energy levels.

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Uwe Grimm, Rudolf A. Roemer, Michael Schreiber, Jian-Xin Zhong. 1999-08-04. Universal level-spacing statistics in quasiperiodic tight-binding models. https://doi.org/10.1016/s0921-5093(00)01173-4

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