Curvature-Induced Geometric Universality in Non-Hermitian Anderson Transitions
Abstract
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≃1 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.
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BibTeX
@misc{wang2026curvatureinduced,
title = {{Curvature-Induced Geometric Universality in Non-Hermitian Anderson Transitions}},
author = {Chen Wang and Run-Qiu Yang and X. R. Wang and Hechen Ren},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09562},
eprint = {2609.09562},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09562},
note = {CC0},
}
RIS
TY - UNPB
TI - Curvature-Induced Geometric Universality in Non-Hermitian Anderson Transitions
AU - Chen Wang
AU - Run-Qiu Yang
AU - X. R. Wang
AU - Hechen Ren
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.09562
UR - https://arxiv.org/abs/2609.09562
AB - 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≃1 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.
ER -