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

Abstract

We investigate the dynamical evolution of a parity-time (PT ) symmetric extension of Aubry-André (AA) model which exhibits the coincidence of localization-delocalization transition point with 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 PT symmetric AA model. The results of the mean displacement show that when the system is in the PT symmetry unbroken regime, the wave packet spreading is ballistic which is different from that in PT symmetry broken regime. Furthermore, we discuss the distinctive features of the Loschmidt echo with the post-quench parameter being localized in different PT symmetric regimes.

Cascade of the delocalization transition in a non-Hermitian interpolating Aubry-Andr{é}-Fibonacci chain

“…Many theoretical quasi-periodic models [1][2][3][4][5][6], including the bichromatic lattices [7], electronic materials in orthogonal magnetic field [9], have been proposed to study the delocalization transition and the critical behavior. In particular, many one-dimensional models have been intensively studied due to its simplicity and experimental realization [10][11][12][13][14][15][16][17][18][19][20][21][22]. Among these models, the Aubry-André model (AA) [1,2,[12][13][14][15][16][17][18] and the Fibonacci model [6,[19][20][21] are two of the most celebrated examples.…”

“…In particular, many one-dimensional models have been intensively studied due to its simplicity and experimental realization [10][11][12][13][14][15][16][17][18][19][20][21][22]. Among these models, the Aubry-André model (AA) [1,2,[12][13][14][15][16][17][18] and the Fibonacci model [6,[19][20][21] are two of the most celebrated examples. For the AA model, the quasiperiodicity enters in the form of an on-site cosine modulation incommensurate with the underlying periodic lattice spacing, and the delocalization transition occurs at a critical value of the quasiperiodic potential [1].…”