Level spacing distribution of localized phases induced by quasiperiodic potentials

Author:

Chao Yang, Yucheng Wang

Keyword:

Condensed Matter, Disordered Systems and Neural Networks, Disordered Systems and Neural Networks (cond-mat.dis-nn), Mathematical Physics (math-ph), Quantum Physics (quant-ph)

journal:

date:

2024-01-18 00:00:00

Abstract

Level statistics is a crucial tool in the exploration of localization physics. The level spacing distribution of localized states in disordered systems follows Poisson statistics, and many studies naturally apply it to the localization induced by quasiperiodic potentials. Taking the Aubry-Andr\'{e} model as an example, we investigate the level spacing distribution of the localized phase caused by quasiperiodic potential. We analytically and numerically calculate its level spacing distribution and find that it does not adhere to Poisson statistics. Moreover, based on this level statistics, we derive the ratio of adjacent gaps and find that for a single sample, it is a $\delta-$function, which is in excellent agreement with numerical studies. Additionally, unlike disordered systems, in quasiperiodic systems, there are variations in the level spacing distribution across different regions of the spectrum, and increasing the size and increasing the sample are non-equivalent. Our findings carry significant implications for the reevaluation of level statistics in quasiperiodic systems and a profound understanding of the distinct effects of quasiperiodic potentials and disorder-induced localization.

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