Accumulation of scale-free localized states induced by local non-Hermiticity

TL;DR

This paper demonstrates that local non-Hermiticity can induce scale-free localization and complex spectral phenomena in Hermitian systems, fundamentally altering their bulk properties and leading to novel phase transitions.

Contribution

It provides exact solutions showing how local non-Hermiticity causes scale-free localization and $ ext{PT}$-symmetry breaking, revealing a new mechanism for bulk property modification.

Findings

Local non-Hermiticity induces scale-free localized states.

System undergoes $ ext{PT}$-symmetry breaking with complex eigenvalues.

Scale-free localization persists even with quasiperiodic disorder.

Abstract

The bulk states of Hermitian systems are believed insensitive to local Hermitian impurities or perturbations except for a few impurity-induced bound states. Thus, it is important to ask whether \textit{local} non-Hermiticity can cause drastic changes to the original Hermitian systems. Here we address this issue affirmatively and present exact solutions for the double chain model with local non-Hermitian terms possessing parity-time ($\mathcal{PT}$) symmetry. Induced by the non-Hermiticity, the system undergoes a sequence of $\mathcal{PT}$-symmetry breakings, after which the eigenenergies appear in complex conjugate pairs. The associated extended bulk states then become scale-free localized and unidirectionally accumulated around the impurity. There exist mobility edges separating the residual extended states until a full scale-free localization of all eigenstates. Further increasing the non-Hermitity counter-intuitively brings the system to a $\mathcal{PT}$-restoration regime with fully real spectra except for a pair of complex bound states. We demonstrate that the local non-Hermiticity generated scale-free localization is a general phenomenon and can even survive the quasiperiodic disorder. Our results indicate that the bulk properties of the original Hermitian system can be globally reshaped by local non-Hermiticity.