Algebraic non-Hermitian skin effect and generalized Fermi surface formula in arbitrary dimensions
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| Format: | Preprint |
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2024
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| _version_ | 1866911101739859968 |
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| 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 |
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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 |