Phase transitions in a non-Hermitian Aubry-André-Harper model

Abstract

The Aubry-André-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 the dynamical behavior of the system, the phase transition is discontinuous when one measures the quantum diffusion exponent δ of wave-packet spreading, with δ = 1 in the delocalized phase V < V c (ballistic transport), δ 1/2 at the critical point V = V c (diffusive transport), and δ = 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-André-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 δ, but also in the speed v of ballistic transport. This means that even very close to the spectral phase transition point, rather counterintuitively, 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.

Floquet engineering of topological localization transitions and mobility edges in one-dimensional non-Hermitian quasicrystals

“…In recent years, the impact of non-Hermiticity on localization transitions in AAH-type and Maryland-type quasicrystals have been explored [78,. The non-Hermitian effects are introduced by either setting the onsite quasiperiodic potential to be non-Hermitian [78,[81][82][83], or making the hopping amplitudes between adjacent lattice sites to be nonreciprocal [84,85]. In these models, it was found that the non-Hermitian terms could induce PT -transitions of the energy spectrum from real to complex (or the opposite), together with localizationdelocalization transitions of the eigenstates.…”

Spectral deformations in non-Hermitian lattices with disorder and skin effect: A solvable model

“…* stefano.longhi@polimi.it Non-Hermiitan skin effect induced by static or fluctuating disorder has been also predicted [14,64,65]. The impact of non-Hermiticity in crystalline systems with disorder has been investigated in several works as well (see, for instance, [68][69][70][71][72][73][74][75][76][77][78][79][80][81][82][83][84][85][86] and references therein). A landmark model revealing the interplay between the skin effect and disorder is provided by the Anderson model of localization in a one-dimensional lattice with asymmetric hopping amplitudes [1,[68][69][70]73], introduced by Hatano and Nelson in a few pioneering works more than two decades ago [68,69].…”

Damping transition in an open generalized Aubry-André-Harper model

“…The Anderson localization can occur for lattice with disorder and long-range aperiodic order [24][25][26][27][28][29]. In recent years, there are growing attentions on the interplay of non-Hermitian physics and disorder effect [30][31][32][33][34][35][36][37][38][39]. One * Electronic address: slzhu@nju.edu.cn line of work is the characterization and classification of matter phase in terms of disorder [16,40,41].…”

“…Other topics concern cooperation with coherent control techniques [42]. Disorder, or quasiperiodicity leads to exotic behaviors, including localization-delocalization transition under the PT symmetry breaking [43][44][45], generalized mobility edges [34] and anomalous particle transport [33], among which the non-Hermitian Aubry-André-Harper (AAH) model provides as a paradigmatic example. However, yet most works only concentrate on non-Hermitian Hamiltonian problems, systems resting on Liouvillians are still rarely studied.…”