Phase transitions in a non-Hermitian Aubry-Andr\'e-Harper model

TL;DR

This paper investigates a non-Hermitian extension of the Aubry-Andre9-Harper model, revealing that the localization-delocalization transition is discontinuous in both diffusion exponent and transport speed, with disorder potentially enhancing transport.

Contribution

It introduces a non-Hermitian version of the Aubry-Andre9-Harper model and demonstrates that the phase transition is discontinuous in dynamical variables, contrasting with the Hermitian case.

Findings

Discontinuous transition in transport speed at the phase boundary.

Ballistic transport persists near the transition point.

Disorder can enhance transport speed in the non-Hermitian model.

Abstract

The Aubry-Andr\'e-Harper model provides a paradigmatic example of aperiodic order in a one-dimensional lattice displaying a delocalization-localization phase transition at a finite critical value $V_c$ of the quasiperiodic potential amplitude $V$. In terms of dynamical behavior of the system, the phase transition is discontinuous when one measures the quantum diffusion exponent $\delta$ of wave packet spreading, with $\delta=1$ in the delocalized phase $V<V_c$ (ballistic transport), $\delta \simeq 1/2$ at the critical point $V=V_c$ (diffusive transport), and $\delta=0$ in the localized phase $V>V_c$ (dynamical localization). However, the phase transition turns out to be smooth when one measures, as a dynamical variable, the speed $v(V)$ of excitation transport in the lattice, which is a continuous function of potential amplitude $V$ and vanishes as the localized phase is approached. Here we consider a non-Hermitian extension of the Aubry-Andr\'e-Harper model, in which hopping along the lattice is asymmetric, and show that the dynamical localization-delocalization transition is discontinuous not only in the diffusion exponent $\delta$, but also in the speed $v$ of ballistic transport. This means that, even very close to the spectral phase transition point, rather counter-intuitively ballistic transport with a finite speed is allowed in the lattice. Also, we show that the ballistic velocity can increase as $V$ is increased above zero, i.e. surprisingly disorder in the lattice can result in an enhancement of transport.