Algebraic non-Hermitian skin effect and generalized Fermi surface formula in arbitrary dimensions

Fuente: arXiv
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Main Authors: Zhang, Kai, Shu, Chang, Sun, Kai
Format: Preprint
Published: 2024
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_version_ 1866911101739859968
author Zhang, Kai
Shu, Chang
Sun, Kai
author_facet Zhang, Kai
Shu, Chang
Sun, Kai
contents The non-Hermitian skin effect, characterized by a proliferation of exponentially localized edge modes in open-boundary systems, has led to the discovery of numerous novel physical phenomena that challenge the limits of conventional band theory. In sharp contrast to this familiar exponential localization, we report a distinct phenomenon--the algebraic non-Hermitian skin effect--which arises generically in non-Hermitian systems with two or more spatial dimensions. In such cases, the amplitude of skin modes typically decays from the boundary following a power law, rather than an exponential form--a behavior not captured by existing theoretical frameworks. To bridge this gap and describe the transition in localization from one to higher dimensions, we develop a generalized Fermi surface framework applicable to open-boundary systems in arbitrary dimensions. This framework not only reproduces known results for the exponential skin effect in 1D, but also predicts a new class of skin effects with algebraic decay in 2D and above. We demonstrate this framework in both tight-binding and continuum models in two and three dimensions. This investigation not only unveils a novel category of the non-Hermitian skin effect but also offers a comprehensive theoretical structure that describes skin effects in any non-Hermitian system, irrespective of its spatial dimensionality.
format Preprint
id arxiv_https___arxiv_org_abs_2406_06682
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Algebraic non-Hermitian skin effect and generalized Fermi surface formula in arbitrary dimensions
Zhang, Kai
Shu, Chang
Sun, Kai
Mesoscale and Nanoscale Physics
Quantum Gases
Optics
Quantum Physics
The non-Hermitian skin effect, characterized by a proliferation of exponentially localized edge modes in open-boundary systems, has led to the discovery of numerous novel physical phenomena that challenge the limits of conventional band theory. In sharp contrast to this familiar exponential localization, we report a distinct phenomenon--the algebraic non-Hermitian skin effect--which arises generically in non-Hermitian systems with two or more spatial dimensions. In such cases, the amplitude of skin modes typically decays from the boundary following a power law, rather than an exponential form--a behavior not captured by existing theoretical frameworks. To bridge this gap and describe the transition in localization from one to higher dimensions, we develop a generalized Fermi surface framework applicable to open-boundary systems in arbitrary dimensions. This framework not only reproduces known results for the exponential skin effect in 1D, but also predicts a new class of skin effects with algebraic decay in 2D and above. We demonstrate this framework in both tight-binding and continuum models in two and three dimensions. This investigation not only unveils a novel category of the non-Hermitian skin effect but also offers a comprehensive theoretical structure that describes skin effects in any non-Hermitian system, irrespective of its spatial dimensionality.
title Algebraic non-Hermitian skin effect and generalized Fermi surface formula in arbitrary dimensions
topic Mesoscale and Nanoscale Physics
Quantum Gases
Optics
Quantum Physics
url https://arxiv.org/abs/2406.06682