Nonmonotonic crossover and scaling behaviors in a disordered 1D quasicrystal

TL;DR

This paper investigates how critical states in a disordered 1D quasicrystal transition to localization, revealing nonmonotonic scaling behaviors and providing analytical insights through renormalization group analysis.

Contribution

It uncovers nonmonotonic re-entrant IPR behavior in disordered quasicrystals and explains it using perturbation renormalization group methods, extending understanding of localization phenomena.

Findings

Most states show increasing IPR with scale

Some states exhibit nonmonotonic IPR behavior

Analytical wavefunctions derived from RG treatment

Abstract

We consider a noninteracting disordered 1D quasicrystal in the weak disorder regime. We show that the critical states of the pure model approach strong localization in strikingly different ways, depending on their renormalization properties. A finite size scaling analysis of the inverse participation ratios of states (IPR) of the quasicrystal shows that they are described by several kinds of scaling functions. While most states show a progressively increasing IPR as a function of the scaling variable, other states exhibit a nonmonotonic `re-entrant' behavior wherein the IPR first decreases, and passes through a minimum, before increasing. This surprising behavior is explained in the framework of perturbation renormalization group treatment, where wavefunctions can be computed analytically as a function of the hopping amplitude ratio and the disorder, however it is not specific to this model. Our results should help to clarify results of recent studies of localization due to random and quasiperiodic potentials.