Non-Abelian Gauge Effect for 2-D Non-Hermitian Hatano-Nelson Model in Cylinder Type
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916800120225792 |
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| author | Zhao, Yiming Miao, Yazhuang Xing, Yihang Qiu, Tianhui Ma, Hongyang Zhao, Xiaolong |
| author_facet | Zhao, Yiming Miao, Yazhuang Xing, Yihang Qiu, Tianhui Ma, Hongyang Zhao, Xiaolong |
| contents | Non-Abelian gauge offers a powerful route to engineer novel topological phenomena. Here, we systematically investigate a two-dimensional (2D) non-Hermitian Hatano-Nelson model incorporating SU(2) non-Abelian gauge, demonstrating the emergence of Hopf-link bulk braiding topology in the complex energy spectrum solely with x-direction nearest-neighbor couplings. Because of the limitations of exceptional point (EP) topology in fully capturing the rich non-Hermitian skin effect (NHSE) under non-Abelian influence, we introduce a novel polarization parameter derived from the generalized Brillouin zone (GBZ). This parameter quantitatively discerns left-, right-, and notably, bipolar skin modes, with its accuracy corroborated by directly encoding real-space eigenstate. Our findings reveal that non-Abelian gauge provides unprecedented influence over NHSE, compared with Abelian gauge and without gauge cases. Furthermore, we uncover unique characteristics of zero-imaginary-energy eigenstates at these topological boundaries, including pronounced degeneracy and bipolar localization which is unaffected by size effects, investigated via dynamical evolution and Inverse Participation Ratio (IPR). This work establishes a new paradigm for synthesizing and manipulating non-Hermitian topological phases driven by non-Abelian structures, opening avenues for topological engineering and holding promise for experimental realization in synthetic dimensional platforms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_08714 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-Abelian Gauge Effect for 2-D Non-Hermitian Hatano-Nelson Model in Cylinder Type Zhao, Yiming Miao, Yazhuang Xing, Yihang Qiu, Tianhui Ma, Hongyang Zhao, Xiaolong Other Condensed Matter Non-Abelian gauge offers a powerful route to engineer novel topological phenomena. Here, we systematically investigate a two-dimensional (2D) non-Hermitian Hatano-Nelson model incorporating SU(2) non-Abelian gauge, demonstrating the emergence of Hopf-link bulk braiding topology in the complex energy spectrum solely with x-direction nearest-neighbor couplings. Because of the limitations of exceptional point (EP) topology in fully capturing the rich non-Hermitian skin effect (NHSE) under non-Abelian influence, we introduce a novel polarization parameter derived from the generalized Brillouin zone (GBZ). This parameter quantitatively discerns left-, right-, and notably, bipolar skin modes, with its accuracy corroborated by directly encoding real-space eigenstate. Our findings reveal that non-Abelian gauge provides unprecedented influence over NHSE, compared with Abelian gauge and without gauge cases. Furthermore, we uncover unique characteristics of zero-imaginary-energy eigenstates at these topological boundaries, including pronounced degeneracy and bipolar localization which is unaffected by size effects, investigated via dynamical evolution and Inverse Participation Ratio (IPR). This work establishes a new paradigm for synthesizing and manipulating non-Hermitian topological phases driven by non-Abelian structures, opening avenues for topological engineering and holding promise for experimental realization in synthetic dimensional platforms. |
| title | Non-Abelian Gauge Effect for 2-D Non-Hermitian Hatano-Nelson Model in Cylinder Type |
| topic | Other Condensed Matter |
| url | https://arxiv.org/abs/2506.08714 |