Dynamical localization in non-Hermitian quasi-crystals

TL;DR

This paper investigates how periodic driving influences localization in one-dimensional non-Hermitian quasi-crystals, revealing critical frequencies and phase shifts that determine localized, delocalized, or mixed phases.

Contribution

It introduces a novel analysis of localization transitions in driven non-Hermitian lattices with incommensurate potentials, identifying critical frequencies and phase shifts affecting spectral properties.

Findings

Two critical driving frequencies identified, one for real spectrum and extended states, another for spectrum disappearance.

Weak complex potential induces localization below a certain driving frequency.

High-frequency limit yields a constant critical phase shift separating real and complex spectra.

Abstract

We study the localization transition in periodically driven one-dimensional non-Hermitian lattices where the piece-wise two-step drive is constituted by uniform coherent tunneling and incommensurate onsite gain and loss. We find that the system can be in localized, delocalized, or mixed-phase depending on the driving frequency and the phase shift of complex potential. Two critical driving frequencies of the system are identified, the first one corresponds to the largest phase shift of the complex potential so that the quasi-energy spectrum is still real and all the states are extended, the second one corresponds to the disappear of full real spectrum, and very weak complex potential leads to the emergence of localized states when the driving frequency is lower than this critical frequency. In the high frequency limit, we find the critical phase shift that separates the two regions with respectively real and complex spectrum tends to a constant value that can be captured by an effective non-Hermitian Hamiltonian.