发表机构
Tianjin University; Chinese University of Hong Kong (Shenzhen)（天津大学; 香港中文大学（深圳））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过双曲晶格上的非厄米安德森转变，发现空间曲率可定义新的普适类，其临界指数接近平均场值，表明曲率是超越维度与对称性的普适性组织原则。
AI 中文摘要
在欧几里得空间中，安德森转变的普适类主要由对称性和空间维度决定。在此，我们为双曲型晶格上的非厄米安德森转变提供了一种由几何控制的普适类的证据。在这种设置下，临界行为受到大尺度双曲几何的影响，其特征为负曲率、指数体积增长以及非欧几里得的空间标度概念。对几种不同的 \\(\{p,q\}\\) 平铺的参与率的有限尺寸标度分析揭示了单参数标度塌缩，其共同临界指数 \\(\nu\simeq1\\) 在数值精度范围内。一个补充的唯象粗粒化朗道-金兹堡分析表明，指数关联体积增长抑制了临界涨落，为观察到的平均场类标度提供了理论依据。我们的结果表明，空间曲率可以作为安德森转变普适性的一个额外组织原则，超越了传统的基于维度和对称性的分类。
英文摘要
In Euclidean space, universality classes of Anderson transitions are primarily determined by symmetry and spatial dimensionality. Here, we present evidence for a geometry-controlled universality class of non-Hermitian Anderson transitions on hyperbolic-like lattices. In this setting, critical behavior is influenced by the large-scale hyperbolic geometry, characterized by negative curvature, exponential volume growth, and a non-Euclidean notion of spatial scaling. Finite-size scaling of participation ratios across several distinct \( \{p,q\} \) tilings reveals one-parameter scaling collapses with a common critical exponent \( ν\simeq1 \) within numerical accuracy. A complementary phenomenological coarse-grained Landau-Ginzburg analysis shows how exponential correlation-volume growth suppresses critical fluctuations, offering a rationale for the observed mean-field-like scaling. Our results suggest that spatial curvature can act as an additional organizing principle for Anderson-transition universality beyond the conventional dimensionality- and symmetry-based classification.
Comments6 pages, 3 figures
