The multiple re-entrant localization in a phase-shift quasiperiodic chain

TL;DR

This paper introduces a phase-shifted quasiperiodic model that demonstrates multiple re-entrant localization phenomena, revealing how phase-shift controls localization and delocalization in the system.

Contribution

It proposes a new phase-shift AAH model to induce and analyze multiple re-entrant localization, providing visualized dynamics and understanding of the underlying mechanisms.

Findings

Multiple re-entrant localization (MREL) occurs due to phase-shift.

Phase-shift enables eigenstates to escape localization.

The model visualizes the transition between localized and extended phases.

Abstract

Inspired by the recently discovered phenomenon of re-entrant localization (REL) [Roy et al., PRL 126, 106803 (2021)], we propose a new approach to induce REL, i.e., to control the quasiperiodic potential's phase-shift between odd and even sites, as thus the system can be dubbed as a phase-shift AAH model. We then analyze the participation ratios and corresponding scaling behaviors, and the results reveal that multiple re-entrant localization (MREL) phenomenon occurs. Furthermore, by depicting the behavior of extension dynamics, we obtain a whole visualized process of the system entering and re-entering the localized phase multiple times. Finally, we exhibit the distribution of quasiperiodic potential with different phase-shift and quasiperiodic parameter, and show the reason for the occurrence of MREL phenomenon, i.e., the introduction of phase-shift enables a part of eigenstates to escape from the localized phase, thus weakening the ``localizibility'' of the system.