Universal level-spacing statistics in quasiperiodic tight-binding models

1999/08/04 by Uwe Grimm, Rudolf A. Römer, Rudolf A. Roemer +3
Materials Science · Physics and Astronomy · #Quantum chaos and dynamical systems #Quasicrystal Structures and Properties #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.mtrl-sci

paper · pdf · doi:10.1016/s0921-5093(00)01173-4

published as Mat. Sci. Eng. A 294-296 (2000) 564-567 · 5 pages, 6 PostScript figures

arxiv created 1999/08/04 · openalex publication_date 2000/12/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Exact eigenstates of tight-binding Hamiltonians on the Penrose tiling
• Energy levels of quasiperiodic Hamiltonians, spectral unfolding, and random matrix theory

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