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Universal level-spacing statistics in quasiperiodic tight-binding models

Grimm, Uwe; Roemer, Rudolf A.; Schreiber, Michael and Zhong, Jian-Xin (2000). Universal level-spacing statistics in quasiperiodic tight-binding models. Materials Science and Engineering A, 294-296 pp. 564–567.

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We studied 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 system 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 fourth neighbour energy levels.

Item Type: Journal Article
ISSN: 0921-5093
Keywords: quasicrystals; electronic properties; tight-binding model; multifractality; energy-level statistics; random matrix theory
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Mathematics, Computing and Technology
Item ID: 12314
Depositing User: Uwe Grimm
Date Deposited: 14 Nov 2008 11:07
Last Modified: 14 Jan 2016 17:27
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