Damping transition in an open generalized Aubry-Andr\'e-Harper model

TL;DR

This paper investigates the damping dynamics and phase transitions in an open generalized Aubry-Andre9-Harper model, revealing boundary-sensitive damping, a skin effect phase transition, and coexistence with Anderson localization, with potential realization in ultracold atoms.

Contribution

It uncovers the phase transition of the non-Hermitian skin effect and the coexistence of skin effect with Anderson localization in an open quasiperiodic system.

Findings

Boundary-sensitive damping dynamics due to the skin effect

Identification of a phase transition with non-Bloch anti-PT symmetry breaking

Coexistence of skin effect and Anderson localization separated by a mobility edge

Abstract

We study the damping dynamics of the single-particle correlation for an open system under periodic and aperiodic order, which is dominated by the Lindblad master equation. In the absence of the aperiodic order, the Liouvillian superoperator exhibits the non-Hermitian skin effect, which leads to unidirectional damping dynamics, dubbed as "chiral damping". Due to the non-Hermitian skin effect, the damping dynamics is boundary sensitive: The long-time damping of such open systems is algebraic under periodic boundary conditions but exponential under open boundary conditions. We reveal the phase transition with the inclusion of the hopping amplitude modulation. By using the spectral topology and a finite-size scaling analysis in the commensurate case, we show there exists a phase transition of the skin effect with non-Bloch anti-parity-time symmetry breaking. For the incommensurate case, we find richer phases with the coexistence of the non-Hermitian skin effect and the Anderson localization, which are separated by a generalized mobility edge. We reveal the transition of the damping dynamics as a consequence of the phase transition. Furthermore, we propose a possible scheme with ultracold atoms in a dissipative momentum lattice to realize and detect the damping dynamics.