Critical analysis of the re-entrant localization transition in a one-dimensional dimerized quasiperiodic lattice

TL;DR

This paper investigates the re-entrant localization transition in a one-dimensional dimerized quasiperiodic lattice, analyzing spectral properties, critical points, and multifractal characteristics to deepen understanding of localization phenomena.

Contribution

It provides a detailed spectral and multifractal analysis of the re-entrant localization transition, including precise critical disorder strengths and critical exponents, advancing the understanding of localization in quasiperiodic systems.

Findings

Identified critical disorder strengths for localization transitions.

Determined critical exponents through finite-size scaling.

Analyzed multifractal properties of states across transitions.

Abstract

A re-entrant localization transition has been predicted recently in a one-dimensional quasiperiodic lattice with dimerized hopping between the nearest-neighbour sites (Phys. Rev. Lett. {\bf 126} 106803 (2021)) \cite{PhysRevLett.126.106803}. It has been shown that the interplay between the hopping dimerization and a staggered quasi-periodic disorder manifests two localization transitions through two intermediate phases resulting in four critical points as a function of the quasiperiodic potential. In this paper, we study the phenomenon of the re-entrant localization transition by examining the spectral properties of the states. By performing a systematic finite-size scaling analysis for a fixed value of the hopping dimerization, we obtain accurate critical disorder strengths for different transitions and the associated critical exponents. Moreover, through a multifractal analysis, we study the critical nature of the states across the localization transitions by computing the mass exponents and the corresponding fractal dimensions of the states. Further, we complement the critical nature of the states by computing the Hausdorff dimensions.