Anderson localization transition in disordered hyperbolic lattices
arXiv:2310.07978 · doi:10.1103/PhysRevLett.133.066101
Abstract
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 and lattices. We find unusually large critical disorder strengths, determine critical exponents, and observe a strong finite-size effect in the level statistics.
main text (5 pages with 3 figures) + bibliography (2 pages) + supplemental material (8 pages with 6 figures and 3 tables)
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