Scaling Theory of the Anderson Transition in Random Graphs: Ergodicity and Universality

García-Mata, I., Giraud, O., Georgeot, B., Martin, J., Dubertrand, Remy and Lemarié, G. (2017) Scaling Theory of the Anderson Transition in Random Graphs: Ergodicity and Universality. Physical Review Letters, 118 (16). p. 166801. ISSN 0031-9007

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We study the Anderson transition on a generic model of random graphs with a tunable branching parameter 1<K<2, through large scale numerical simulations and finite-size scaling analysis. We find that a single transition separates a localized phase from an unusual delocalized phase that is ergodic at large scales but strongly nonergodic at smaller scales. In the critical regime, multifractal wave functions are located on a few branches of the graph. Different scaling laws apply on both sides of the transition: a scaling with the linear size of the system on the localized side, and an unusual volumic scaling on the delocalized side. The critical scalings and exponents are independent of the branching parameter, which strongly supports the universality of our results.

Item Type: Article
Subjects: F300 Physics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Related URLs:
Depositing User: Elena Carlaw
Date Deposited: 20 Nov 2019 10:49
Last Modified: 31 Jul 2021 20:33

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