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 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-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 $\delta$, 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.

10 pages, 6 figures, to appear in Phys. Rev. B

References in corpus (6)

• Efficient Light Funneling based on the non-Hermitian Skin Effect
• Topological phase transition in non-Hermitian quasicrystals
• The quasi-periodic Bose-Hubbard model and localization in one-dimensional cold atomic gases
• Disorder-induced enhancement of transport through graphene p-n junctions
• Light Localization induced by Random Imaginary Permittivities
• Disorder effect on the localization/delocalization in incommensurate potential

Cited by in corpus (9)

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• Floquet engineering of topological localization transitions and mobility edges in one-dimensional non-Hermitian quasicrystals
• Quantum Entanglement of Non-Hermitian Quasicrystals
• Non-Hermitian Maryland Model
• Breakdown of the correspondence between the real-complex and delocalization-localization transitions in non-Hermitian quasicrystals
• Quantum criticality and universality in the $p$-wave paired Aubry-André-Harper model
• Two-dimensional anisotropic non-Hermitian Lieb lattice
• Probing the superfluid-insulator phase transition by a non-Hermitian external field
• Phase transitions in non-Hermitian superlattices