Anderson localization transition in disordered hyperbolic lattices
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909289607593984 |
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| author | Chen, Anffany Maciejko, Joseph Boettcher, Igor |
| author_facet | Chen, Anffany Maciejko, Joseph Boettcher, Igor |
| contents | We study Anderson localization in disordered tight-binding models on hyperbolic lattices. Such lattices are geometries intermediate between ordinary two-dimensional crystalline lattices, which localize at infinitesimal disorder, and Bethe lattices, which localize at strong disorder. Using state-of-the-art computational group theory methods to create large systems, we approximate the thermodynamic limit through appropriate periodic boundary conditions and numerically demonstrate the existence of an Anderson localization transition on the $\{8,3\}$ and $\{8,8\}$ lattices. We find unusually large critical disorder strengths, determine critical exponents, and observe a strong finite-size effect in the level statistics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_07978 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Anderson localization transition in disordered hyperbolic lattices Chen, Anffany Maciejko, Joseph Boettcher, Igor Disordered Systems and Neural Networks Mesoscale and Nanoscale Physics Statistical Mechanics Strongly Correlated Electrons Mathematical Physics We study Anderson localization in disordered tight-binding models on hyperbolic lattices. Such lattices are geometries intermediate between ordinary two-dimensional crystalline lattices, which localize at infinitesimal disorder, and Bethe lattices, which localize at strong disorder. Using state-of-the-art computational group theory methods to create large systems, we approximate the thermodynamic limit through appropriate periodic boundary conditions and numerically demonstrate the existence of an Anderson localization transition on the $\{8,3\}$ and $\{8,8\}$ lattices. We find unusually large critical disorder strengths, determine critical exponents, and observe a strong finite-size effect in the level statistics. |
| title | Anderson localization transition in disordered hyperbolic lattices |
| topic | Disordered Systems and Neural Networks Mesoscale and Nanoscale Physics Statistical Mechanics Strongly Correlated Electrons Mathematical Physics |
| url | https://arxiv.org/abs/2310.07978 |