Level-Spacing Distributions of Planar Quasiperiodic Tight-Binding Models

TL;DR

This paper analyzes the energy spectra of two-dimensional quasiperiodic tight-binding models, showing their level-spacing distributions align with random matrix theory and differ from those at the metal-insulator transition in disordered systems.

Contribution

It demonstrates that quasiperiodic models exhibit universal Wigner-Dyson level-spacing distributions when symmetries are properly considered.

Findings

Level-spacing distributions match Wigner-Dyson distribution

Differences observed between Wigner surmise and exact distributions

Distinct from distributions at the 3D Anderson transition

Abstract

We study the statistical properties of energy spectra of two-dimensional quasiperiodic tight-binding models. We demonstrate that the nearest-neighbor level spacing distributions of these non-random systems are well described by random matrix theory. Properly taking into account the symmetries of models defined on various finite approximants of quasiperiodic tilings, we find that the underlying universal level-spacing distribution is given by the Wigner-Dyson distribution of the Gaussian orthogonal random matrix ensemble. Our data allow us to see the differences between the Wigner surmise and the exact level-spacing distribution. In particular, our result differs from the critical level-spacing distribution computed at the metal-insulator transition in the three-dimensional Anderson model of disorder.