Universal level-spacing statistics in quasiperiodic tight-binding models

TL;DR

This study investigates the spectral statistics of 2D quasiperiodic tight-binding models, revealing that their level-spacing distributions follow universal patterns akin to Gaussian orthogonal ensembles, despite multifractal eigenstates.

Contribution

It demonstrates that quasiperiodic models exhibit universal level-spacing statistics similar to random matrix theory, contrasting with expected critical statistics.

Findings

Level-spacing distributions match Gaussian orthogonal ensemble predictions

Eigenstates exhibit multifractality confirmed by participation number scaling

Spectral statistics are universal across different quasiperiodic models

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.