Anomalous spectrum in a non-Hermitian quasiperiodic chain

TL;DR

This paper investigates a one-dimensional non-Hermitian quasiperiodic lattice with long-range hopping, revealing an unusual spectral phase where localized and extended states are intermixed, leading to complex energy behaviors.

Contribution

It demonstrates the existence of an anomalous spectral intermixing phase in non-Hermitian quasiperiodic systems, extending understanding of spectral properties beyond traditional localization and extension.

Findings

Localized and extended states are intermixed in the spectrum.

An intermediate phase with paired extended states appears.

Complex energies can encircle real energies in the spectrum.

Abstract

The spectra of particles in disordered lattices can either be completely extended or localized or can be intermediate which hosts both the localized and extended states separated from each other. In this work, however, we show that in the case of a one dimensional lattice with long-range hopping and non-Hermitian quasiperiodic onsite potential, the localized and extended states in the spectrum are intermixed with each other rather than well separated. As a result, an atypical intermediate phase appears where consecutive pairs of extended states intermittently appear in the pool of localized states. We also argue that such anomalous spectral intermixing can be realized in the short-range hopping limit by appropriate engineering of the onsite potential. Moreover, we obtain that the nature of the spectrum also reveals non-standard scenarios in the complex energy plane where the complex energies encircle real ones. These findings shed light on the intricate interplay between the non-Hermiticity and quasiperiodic disorder in the system.