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

• URL: http://arxiv.org/abs/2302.02798v3
• Date: Sun, 30 Apr 2023 08:30:15 GMT
• Title: Accumulation of scale-free localized states induced by local non-Hermiticity
• Authors: Cui-Xian Guo, Xueliang Wang, Haiping Hu, Shu Chen
• Abstract summary: We show 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.
• Score: 1.2514666672776884
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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