Geometric origin of self-intersection points in non-Hermitian energy spectra
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915235407855616 |
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| author | Pi, Jinghui Wang, Chenyang Liu, Yong-Chun Yan, Yangqian |
| author_facet | Pi, Jinghui Wang, Chenyang Liu, Yong-Chun Yan, Yangqian |
| contents | Unlike Hermitian systems, non-Hermitian energy spectra under periodic boundary conditions can form closed loops in the complex energy plane, a phenomenon known as point gap topology. In this paper, we investigate the self-intersection points of such non-Hermitian energy spectra and reveal their geometric origins. We rigorously demonstrate that these self-intersection points result from the intersection of the auxiliary generalized Brillouin zone and the Brillouin zone in one-band systems, as confirmed by an extended Hatano-Nelson model. This finding is further generalized to multi-band systems, illustrated through a non-Hermitian Su-Schrieffer-Heeger model. Moreover, we address multiple self-intersection points and derive the geometric conditions for general n-fold self-intersection points. Our results enhance the fundamental understanding of generic non-Hermitian quantum systems and provide theoretical support for further experimental investigations of energy self-intersection points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_04755 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometric origin of self-intersection points in non-Hermitian energy spectra Pi, Jinghui Wang, Chenyang Liu, Yong-Chun Yan, Yangqian Quantum Physics Quantum Gases Optics Unlike Hermitian systems, non-Hermitian energy spectra under periodic boundary conditions can form closed loops in the complex energy plane, a phenomenon known as point gap topology. In this paper, we investigate the self-intersection points of such non-Hermitian energy spectra and reveal their geometric origins. We rigorously demonstrate that these self-intersection points result from the intersection of the auxiliary generalized Brillouin zone and the Brillouin zone in one-band systems, as confirmed by an extended Hatano-Nelson model. This finding is further generalized to multi-band systems, illustrated through a non-Hermitian Su-Schrieffer-Heeger model. Moreover, we address multiple self-intersection points and derive the geometric conditions for general n-fold self-intersection points. Our results enhance the fundamental understanding of generic non-Hermitian quantum systems and provide theoretical support for further experimental investigations of energy self-intersection points. |
| title | Geometric origin of self-intersection points in non-Hermitian energy spectra |
| topic | Quantum Physics Quantum Gases Optics |
| url | https://arxiv.org/abs/2502.04755 |