Reentrant Localization in Quasiperiodic Thue-Morse Chain

TL;DR

This paper studies a quasiperiodic SSH chain with Thue-Morse sequence modulation, revealing reentrant localization behavior and phase transitions between extended, multifractal, and localized states, controllable by system parameters.

Contribution

It introduces a deterministic, quasiperiodic model exhibiting reentrant localization, expanding understanding of phase behavior in non-random systems.

Findings

Reentrant localization behavior observed with increasing quasiperiodic amplitude.

Phase diagram showing boundaries between extended, multifractal, and localized regimes.

Control over critical thresholds via tuning system parameters.

Abstract

We investigate localization and reentrance in a dimerized Su-Schrieffer-Heeger (SSH) tight-binding chain whose on-site energies are given by a quasiperiodic cosine masked by a deterministic Thue-Morse sequence. Working with non-interacting, spinless fermions, we solve the model via exact diagonalization on large Fibonacci sizes and diagnose phases using inverse/normalized participation ratios and the correlation fractal dimension. We identify boundaries separating extended, multifractal (mixed), and localized regimes by constructing a phase diagram in the plane of modulation strength and dimerization ratio. As the quasiperiodic amplitude is increased, the system exhibits reentrant behavior, localizing, partially re-delocalizing into a multifractal regime, and re-localizing, verified via two-size crossings of band-averaged observables and finite-size scaling. We demonstrate that tuning the modulation strength, the SSH dimerization, or the incommensurability parameter provides control over the critical thresholds. Our results suggest a versatile, randomness-free platform for the deterministic control of transport, enabling switching between conducting, multifractal, and insulating states.