Anomalous localization enhancement in one-dimensional non-Hermitian disordered lattices

TL;DR

This paper investigates how non-Hermitian disorder in a one-dimensional lattice leads to enhanced localization of eigenstates, especially at the band center, revealing strong anomalous Anderson localization phenomena.

Contribution

It demonstrates that non-Hermitian disorder causes all eigenstates to localize in the thermodynamic limit, with pronounced localization near the band center, a novel finding in disordered non-Hermitian systems.

Findings

Eigenstates are localized in the thermodynamic limit with imaginary disorder.

Strong anomalous localization occurs at the band center.

Presence of many strongly-localized states with imaginary eigenvalues.

Abstract

We study numerically the localization properties of eigenstates in a one-dimensional random lattice described by a non-Hermitian disordered Hamiltonian, where both the disorder and the non-Hermiticity are inserted simultaneously in the on-site potential. We calculate the averaged participation number, the Shannon entropy and the structural entropy as a function of other parameters. We show that, in the presence of an imaginary random potential, all eigenstates are localized in the thermodynamic limit and strong anomalous Anderson localization occurs at the band center. In contrast to the usual localization anomalies where a weaker localization is observed, the localization of the eigenstates near the band center is strongly enhanced in the present non-Hermitian model. This phenomenon is associated with the occurrence of a large number of strongly-localized states with pure imaginary energy eigenvalues.