Scale-free localization and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="script">PT</mml:mi></mml:math> symmetry breaking from local non-Hermiticity
Bo Li, He-Ran Wang, Fei Song, Zhong Wang
Abstract
We show that a local non-Hermitian perturbation in a Hermitian lattice system generically induces scale-free localization for the continuous-spectrum eigenstates. When the perturbation lies at a finite distance to the boundary, the scale-free eigenstates are promoted to exponentially localized modes, whose number is proportional to the distance. Furthermore, when the local non-Hermitian perturbation respects parity-time $(\mathcal{PT})$ symmetry, the $\mathcal{PT}$ symmetry breaking is always accompanied by the emergence of scale-free or exponential localization. Intriguingly, we find a concise band-structure condition which tells not only when the continuous-spectrum $\mathcal{PT}$ breaking of scale-free modes can occur but also the precise $\mathcal{PT}$-breaking energy window. Our results uncover a series of unexpected generic phenomena induced by a local non-Hermitian perturbation, which has interesting interplay with $\mathcal{PT}$ symmetry.