Theory of Anderson localization on the hyperbolic plane
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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_ | 1866915961998671872 |
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| author | Altland, Alexander Micklitz, Tobias Sharma, Devasheesh Usoltcev, Maksimilian Wille, Carolin |
| author_facet | Altland, Alexander Micklitz, Tobias Sharma, Devasheesh Usoltcev, Maksimilian Wille, Carolin |
| contents | The two-dimensional hyperbolic plane, $\mathbb{H}^2$, is an unusual system in that dimensionality changes with scale: locally two-dimensional and planar at short distances, but effectively infinite-dimensional at large scales, it provides an interesting paradigm for the study of (quantum) phase transitions, notably the disorder-driven Anderson transition. Generalizing previous work, which treated short and large distance scales separately, we develop a unified framework interpolating between the principles of low- and high-dimensional Anderson localization. As a main result, we derive a two-parameter flow in a plane spanned by scale-dependent curvature (setting the system's effective dimensionality) and conductivity, with an extended critical line separating metallic and insulating phases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24917 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Theory of Anderson localization on the hyperbolic plane Altland, Alexander Micklitz, Tobias Sharma, Devasheesh Usoltcev, Maksimilian Wille, Carolin Disordered Systems and Neural Networks High Energy Physics - Theory The two-dimensional hyperbolic plane, $\mathbb{H}^2$, is an unusual system in that dimensionality changes with scale: locally two-dimensional and planar at short distances, but effectively infinite-dimensional at large scales, it provides an interesting paradigm for the study of (quantum) phase transitions, notably the disorder-driven Anderson transition. Generalizing previous work, which treated short and large distance scales separately, we develop a unified framework interpolating between the principles of low- and high-dimensional Anderson localization. As a main result, we derive a two-parameter flow in a plane spanned by scale-dependent curvature (setting the system's effective dimensionality) and conductivity, with an extended critical line separating metallic and insulating phases. |
| title | Theory of Anderson localization on the hyperbolic plane |
| topic | Disordered Systems and Neural Networks High Energy Physics - Theory |
| url | https://arxiv.org/abs/2604.24917 |