Localization transitions in an open quasiperiodic ladder

TL;DR

This paper explores how dissipation influences localization transitions in a quasiperiodic ladder, revealing that dissipation can induce mixed phases and reshape localization behavior in non-Hermitian quantum systems.

Contribution

It demonstrates that dissipation can induce a mixed-phase zone in a 1D quasiperiodic system without explicit constraints, using an exact Liouvillian-Hamiltonian correspondence and third quantization.

Findings

Dissipation induces a mixed-phase zone in the system.

The mixed-phase zone appears with imbalance but not with balanced dissipation.

The width and critical points of the mixed phase are tunable via dissipation strength.

Abstract

We investigate localization transition in an open quasiperiodic ladder where the quasiperiodicity is described by the Aubry-Andr\'e-Harper model. While previous studies have shown that higher-order hopping or constrained quasiperiodic potentials can induce a mixed-phase zone in one dimension, we demonstrate that the dissipation can induce mixed phase zone in a one dimensional nearest-neighbor system without imposing any explicit constraints on the quasiperiodic potential or hopping parameter. Our approach exploits an exact correspondence between the eigenspectrum of the Liouvillian superoperator and that of the non-Hermitian Hamiltonian, valid for quadratic fermionic systems under linear dissipation. Using third quantization approach within Majorana fermionic representation, we analyze two dissipation configurations: alternating gain and loss at every site, and at alternate sites under balanced and imbalanced conditions. By computing the inverse and normalized participation ratios, we show that dissipation can drive the system into three distinct phases: delocalizd, mixed, and localized. Notably, the mixed-phase zone is absent for balanced dissipation at every site but emerges upon introducing imbalance, while for alternate site dissipation it appears in both balanced and imbalanced cases. Furthermore, the critical points and the width of the mixed-phase window can be selectively tuned by varying the dissipation strength. These findings reveal that the dissipation plays a decisive role in reshaping localization transitions in quasiperiodic systems, offering new insight into the interplay between non-Hermitian effects and quasiperiodic order.