Non-Hermitian Twisting Theory under the open boundary condition
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910254077313024 |
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| author | Zhao, Chen-Hao Li, Jia-Rui Tian, Yuping Gong, Wei-Jiang |
| author_facet | Zhao, Chen-Hao Li, Jia-Rui Tian, Yuping Gong, Wei-Jiang |
| contents | The non-Hermitian skin effect (NHSE) is a hallmark of non-Hermitian system, yet its generalized Brillouin zone (GBZ) description is restricted to periodic systems. We develop a site-resolved theory via a local scaling transformation (LST), introducing local twisting $T_n$ to quantify metric operator $ξ$ nontriviality. This elucidates the NHSE's origin and uncovers the generalized multiple-channel skin effect (MCSE). Exploiting $T_n$'s translational independence, we define the Zahlen-Brillouin Zone (ZBZ), extending non-Hermitian band theory to nonperiodic and disordered lattices. Furthermore, we unify the $ξ$ with GBZ Riemannian geometry, establishing the metric and state correspondence (MSC) as the principle for real-space localization. With a global skin index $\mathbfΓ$ for phase transitions, our results provide a universal paradigm for non-Hermitian physics in both crystalline and amorphous media. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_25386 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-Hermitian Twisting Theory under the open boundary condition Zhao, Chen-Hao Li, Jia-Rui Tian, Yuping Gong, Wei-Jiang Mesoscale and Nanoscale Physics Quantum Physics The non-Hermitian skin effect (NHSE) is a hallmark of non-Hermitian system, yet its generalized Brillouin zone (GBZ) description is restricted to periodic systems. We develop a site-resolved theory via a local scaling transformation (LST), introducing local twisting $T_n$ to quantify metric operator $ξ$ nontriviality. This elucidates the NHSE's origin and uncovers the generalized multiple-channel skin effect (MCSE). Exploiting $T_n$'s translational independence, we define the Zahlen-Brillouin Zone (ZBZ), extending non-Hermitian band theory to nonperiodic and disordered lattices. Furthermore, we unify the $ξ$ with GBZ Riemannian geometry, establishing the metric and state correspondence (MSC) as the principle for real-space localization. With a global skin index $\mathbfΓ$ for phase transitions, our results provide a universal paradigm for non-Hermitian physics in both crystalline and amorphous media. |
| title | Non-Hermitian Twisting Theory under the open boundary condition |
| topic | Mesoscale and Nanoscale Physics Quantum Physics |
| url | https://arxiv.org/abs/2605.25386 |