Non-Hermitian Skin Effect Along Hyperbolic Geodesics
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917809974411264 |
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| author | Shen, Ruizhe Chan, Wei Jie Lee, Ching Hua |
| author_facet | Shen, Ruizhe Chan, Wei Jie Lee, Ching Hua |
| contents | Recently, it has been revealed that a variety of novel phenomena emerge in hyperbolic spaces, while non-Hermitian physics has significantly enriched the landscape of condensed matter physics. Building on these developments, we construct a geodesic-based method to study the non-Hermitian skin effect (NHSE) in non-reciprocal hyperbolic lattices. Additionally, we develop a geodesic-periodic boundary condition (geodesic-PBC), akin to the Euclidean periodic boundary condition (PBC), that complements its open boundary condition. Importantly, we find that the non-reciprocal directionality within a hyperbolic regular polygon and the geodesic-based boundary determine the spectral sensitivity, and hence, the NHSE. Unlike in Euclidean models, however, we must utilize boundary localization to distinguish non-trivial skin modes from their trivial boundary counterpart due to the extensive boundary volume of hyperbolic lattices. We also relate the spatial density profile with the finite-size scaling of hyperbolic lattices. These aspects highlight the profound impact of hyperbolic geometry on non-Hermitian systems and offer new perspectives on the intricate relationship between the geometric characteristics of hyperbolic lattices and non-Hermitian physics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_15278 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-Hermitian Skin Effect Along Hyperbolic Geodesics Shen, Ruizhe Chan, Wei Jie Lee, Ching Hua Other Condensed Matter Mesoscale and Nanoscale Physics Recently, it has been revealed that a variety of novel phenomena emerge in hyperbolic spaces, while non-Hermitian physics has significantly enriched the landscape of condensed matter physics. Building on these developments, we construct a geodesic-based method to study the non-Hermitian skin effect (NHSE) in non-reciprocal hyperbolic lattices. Additionally, we develop a geodesic-periodic boundary condition (geodesic-PBC), akin to the Euclidean periodic boundary condition (PBC), that complements its open boundary condition. Importantly, we find that the non-reciprocal directionality within a hyperbolic regular polygon and the geodesic-based boundary determine the spectral sensitivity, and hence, the NHSE. Unlike in Euclidean models, however, we must utilize boundary localization to distinguish non-trivial skin modes from their trivial boundary counterpart due to the extensive boundary volume of hyperbolic lattices. We also relate the spatial density profile with the finite-size scaling of hyperbolic lattices. These aspects highlight the profound impact of hyperbolic geometry on non-Hermitian systems and offer new perspectives on the intricate relationship between the geometric characteristics of hyperbolic lattices and non-Hermitian physics. |
| title | Non-Hermitian Skin Effect Along Hyperbolic Geodesics |
| topic | Other Condensed Matter Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2410.15278 |