General theory for geometry-dependent non-Hermitian bands
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909890469953536 |
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| author | Wang, Chenyang Pi, Jinghui Liu, Qinxin Li, Yaohua Liu, Yong-Chun |
| author_facet | Wang, Chenyang Pi, Jinghui Liu, Qinxin Li, Yaohua Liu, Yong-Chun |
| contents | In two- and higher-dimensional non-Hermitian lattices, systems can exhibit geometry-dependent bands, where the spectrum and eigenstates under open boundary conditions depend on the bulk geometry even in the thermodynamic limit. Although geometry-dependent bands are widely observed, the underlying mechanism for this phenomenon remains unclear. In this work, we address this problem by establishing a higher-dimensional non-Bloch band theory based on the concept of "strip generalized Brillouin zones" (SGBZs), which describe the asymptotic behavior of non-Hermitian bands when a lattice is extended sequentially along its linearly independent axes. Within this framework, we demonstrate that geometry-dependent bands arise from the incompatibility of SGBZs and, for the first time, derive a general criterion for the geometry dependence of non-Hermitian bands: non-zero area of the complex energy spectrum or the imaginary momentum spectrum. Our work opens an avenue for future studies on the interplay between geometric effects and non-Hermitian physics, such as non-Hermitian band topology. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_22743 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | General theory for geometry-dependent non-Hermitian bands Wang, Chenyang Pi, Jinghui Liu, Qinxin Li, Yaohua Liu, Yong-Chun Mesoscale and Nanoscale Physics Quantum Gases Mathematical Physics Optics Quantum Physics In two- and higher-dimensional non-Hermitian lattices, systems can exhibit geometry-dependent bands, where the spectrum and eigenstates under open boundary conditions depend on the bulk geometry even in the thermodynamic limit. Although geometry-dependent bands are widely observed, the underlying mechanism for this phenomenon remains unclear. In this work, we address this problem by establishing a higher-dimensional non-Bloch band theory based on the concept of "strip generalized Brillouin zones" (SGBZs), which describe the asymptotic behavior of non-Hermitian bands when a lattice is extended sequentially along its linearly independent axes. Within this framework, we demonstrate that geometry-dependent bands arise from the incompatibility of SGBZs and, for the first time, derive a general criterion for the geometry dependence of non-Hermitian bands: non-zero area of the complex energy spectrum or the imaginary momentum spectrum. Our work opens an avenue for future studies on the interplay between geometric effects and non-Hermitian physics, such as non-Hermitian band topology. |
| title | General theory for geometry-dependent non-Hermitian bands |
| topic | Mesoscale and Nanoscale Physics Quantum Gases Mathematical Physics Optics Quantum Physics |
| url | https://arxiv.org/abs/2506.22743 |