Fragile non-Bloch spectrum and unconventional Green's function

Fuente: arXiv
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Autori principali: Song, Fei, Wang, Hong-Yi, Wang, Zhong
Natura: Preprint
Pubblicazione: 2024
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author Song, Fei
Wang, Hong-Yi
Wang, Zhong
author_facet Song, Fei
Wang, Hong-Yi
Wang, Zhong
contents In non-Hermitian systems, it is a counterintuitive feature of the non-Hermitian skin effect (NHSE) that the energy spectrum and eigenstates can be totally different under open or periodic boundary conditions, suggesting that non-Hermitian spectra can be extremely sensitive to non-local perturbations. Here, we show that a wide range of non-Hermitian models with NHSE can even be highly sensitive to local perturbation under open boundary conditions. The spectrum of these models is so fragile that it can be significantly modified by adding only exponentially small perturbations on boundaries. Intriguingly, we show that such fragile spectra are quantified by the Green's function exhibiting unconventional V-shape asymptotic behaviors. Accordingly, bi-directional exponential amplification can be observed. As an interesting consequence, we find a real-to-complex transition of the bulk spectrum induced by exponentially small boundary perturbations. Finally, we reveal a hierarchy of the asymptotic behaviors of non-Hermitian Green's functions, which restricts the frequency range for the presence of unconventional Green's functions.
format Preprint
id arxiv_https___arxiv_org_abs_2410_23175
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Fragile non-Bloch spectrum and unconventional Green's function
Song, Fei
Wang, Hong-Yi
Wang, Zhong
Quantum Physics
Mesoscale and Nanoscale Physics
Quantum Gases
Optics
In non-Hermitian systems, it is a counterintuitive feature of the non-Hermitian skin effect (NHSE) that the energy spectrum and eigenstates can be totally different under open or periodic boundary conditions, suggesting that non-Hermitian spectra can be extremely sensitive to non-local perturbations. Here, we show that a wide range of non-Hermitian models with NHSE can even be highly sensitive to local perturbation under open boundary conditions. The spectrum of these models is so fragile that it can be significantly modified by adding only exponentially small perturbations on boundaries. Intriguingly, we show that such fragile spectra are quantified by the Green's function exhibiting unconventional V-shape asymptotic behaviors. Accordingly, bi-directional exponential amplification can be observed. As an interesting consequence, we find a real-to-complex transition of the bulk spectrum induced by exponentially small boundary perturbations. Finally, we reveal a hierarchy of the asymptotic behaviors of non-Hermitian Green's functions, which restricts the frequency range for the presence of unconventional Green's functions.
title Fragile non-Bloch spectrum and unconventional Green's function
topic Quantum Physics
Mesoscale and Nanoscale Physics
Quantum Gases
Optics
url https://arxiv.org/abs/2410.23175