Dynamical evolution in a one-dimensional incommensurate lattice with $\mathcal{PT}$ symmetry

TL;DR

This paper studies the dynamical behavior of a $ ext{PT}$-symmetric extension of the Aubry-Andre9 model, revealing how localization and symmetry-breaking influence wave packet spreading and Loschmidt echo features.

Contribution

It introduces a $ ext{PT}$-symmetric Aubry-Andre9 model and analyzes its dynamical evolution, highlighting the connection between $ ext{PT}$ symmetry breaking and localization-delocalization transitions.

Findings

Ballistic wave-packet spreading in the $ ext{PT}$ unbroken regime

Distinctive features of Loschmidt echo depending on $ ext{PT}$ regime

Localization-delocalization transition coincides with $ ext{PT}$ symmetry breaking point

Abstract

We investigate the dynamical evolution of a parity-time ($\mathcal{PT}$) symmetric extension of the Aubry-Andr\'{e} (AA) model, which exhibits the coincidence of a localization-delocalization transition point with a $\mathcal{PT}$ symmetry breaking point. One can apply the evolution of the profile of the wave packet and the long-time survival probability to distinguish the localization regimes in the $\mathcal{PT}$ symmetric AA model. The results of the mean displacement show that when the system is in the $\mathcal{PT}$ symmetry unbroken regime, the wave-packet spreading is ballistic, which is different from that in the $\mathcal{PT}$ symmetry broken regime. Furthermore, we discuss the distinctive features of the Loschmidt echo with the post-quench parameter being localized in different $\mathcal{PT}$ symmetric regimes.