Two-dimensional Asymptotic Generalized Brillouin Zone Theory
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866911757995343872 |
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| author | Xu, Zeqi Pang, Bo Zhang, Kai Yang, Zhesen |
| author_facet | Xu, Zeqi Pang, Bo Zhang, Kai Yang, Zhesen |
| contents | In this work, we propose a theory on the two-dimensional non-Hermitian skin effect by resolving two representative minimal models. Specifically, we show that for any given non-Hermitian Hamiltonian, (i) the corresponding region covered by its open boundary spectrum on the complex energy plane should be independent of the open boundary geometry; and (ii) for any given open boundary eigenvalue $E_0$ , its corresponding two-dimensional asymptotic generalized Brillouin zone is determined by a series of geometry-independent Bloch/non-Bloch Fermi points and geometry-dependent non-Bloch equal frequency contours that connect them. A corollary of our theory is that most symmetry-protected exceptional semimetals should be robust to variations in OBC geometry. Our theory paves the way to the discussion on the higher dimensional non-Bloch band theory and the corresponding non-Hermitian bulk-boundary correspondence. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_16868 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Two-dimensional Asymptotic Generalized Brillouin Zone Theory Xu, Zeqi Pang, Bo Zhang, Kai Yang, Zhesen Mesoscale and Nanoscale Physics Quantum Gases Quantum Physics In this work, we propose a theory on the two-dimensional non-Hermitian skin effect by resolving two representative minimal models. Specifically, we show that for any given non-Hermitian Hamiltonian, (i) the corresponding region covered by its open boundary spectrum on the complex energy plane should be independent of the open boundary geometry; and (ii) for any given open boundary eigenvalue $E_0$ , its corresponding two-dimensional asymptotic generalized Brillouin zone is determined by a series of geometry-independent Bloch/non-Bloch Fermi points and geometry-dependent non-Bloch equal frequency contours that connect them. A corollary of our theory is that most symmetry-protected exceptional semimetals should be robust to variations in OBC geometry. Our theory paves the way to the discussion on the higher dimensional non-Bloch band theory and the corresponding non-Hermitian bulk-boundary correspondence. |
| title | Two-dimensional Asymptotic Generalized Brillouin Zone Theory |
| topic | Mesoscale and Nanoscale Physics Quantum Gases Quantum Physics |
| url | https://arxiv.org/abs/2311.16868 |