Unveiling Non-Hermitian Spectral Topology in Hyperbolic Lattices with Non-Abelian Translation Symmetry
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| Format: | Preprint |
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2024
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| _version_ | 1866908562365612032 |
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| author | Hu, Mengying Lin, Jing Ding, Kun |
| author_facet | Hu, Mengying Lin, Jing Ding, Kun |
| contents | The hyperbolic lattice (HBL) has emerged as a compelling platform for exploring matter in non-Euclidean space. Among its notable features, the breakdown of the conventional Bloch theorem stands out, prompting a reexamination of band theory, with the determination of spectra for non-Hermitian systems being a prominent example. Here, we develop an approach to determining the spectra under open boundary conditions (OBCs), one of the foundations in non-Hermitian lattices, from the reciprocal space of HBLs. By introducing supercells to encompass states that are allowed by non-Abelian translational groups, we perform analytic continuation and base on the point gap topology to acquire uniform spectra, the universal OBC spectral range. Applying this method to a single-band nonreciprocal model and a reciprocal non-Abelian semimetal model, we reveal higher-dimensional skin effects and topological phase transitions, respectively, demonstrating the feasibility of our method in predicting spectral topology and investigating non-Hermitian physics in HBLs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_05607 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unveiling Non-Hermitian Spectral Topology in Hyperbolic Lattices with Non-Abelian Translation Symmetry Hu, Mengying Lin, Jing Ding, Kun Mesoscale and Nanoscale Physics Other Condensed Matter Classical Physics Quantum Physics The hyperbolic lattice (HBL) has emerged as a compelling platform for exploring matter in non-Euclidean space. Among its notable features, the breakdown of the conventional Bloch theorem stands out, prompting a reexamination of band theory, with the determination of spectra for non-Hermitian systems being a prominent example. Here, we develop an approach to determining the spectra under open boundary conditions (OBCs), one of the foundations in non-Hermitian lattices, from the reciprocal space of HBLs. By introducing supercells to encompass states that are allowed by non-Abelian translational groups, we perform analytic continuation and base on the point gap topology to acquire uniform spectra, the universal OBC spectral range. Applying this method to a single-band nonreciprocal model and a reciprocal non-Abelian semimetal model, we reveal higher-dimensional skin effects and topological phase transitions, respectively, demonstrating the feasibility of our method in predicting spectral topology and investigating non-Hermitian physics in HBLs. |
| title | Unveiling Non-Hermitian Spectral Topology in Hyperbolic Lattices with Non-Abelian Translation Symmetry |
| topic | Mesoscale and Nanoscale Physics Other Condensed Matter Classical Physics Quantum Physics |
| url | https://arxiv.org/abs/2412.05607 |