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arXiv · 2604.24917

Theory of Anderson localization on the hyperbolic plane

Alexander Altland·Tobias Micklitz·Devasheesh Sharma·Maksimilian Usoltcev·Carolin Wille
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Abstract

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.

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Alexander Altland, Tobias Micklitz, Devasheesh Sharma, Maksimilian Usoltcev, Carolin Wille. 2026-04-27. Theory of Anderson localization on the hyperbolic plane. https://arxiv.org/abs/2604.24917

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