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

Ignacio Garcia-Mata, Olivier Giraud, Bertrand Georgeot, John Martin, Remy Dubertrand, G. Lemarie

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60 Citations (Scopus)
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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.
Original languageEnglish
Article number166801
JournalPhysical Review Letters
Issue number16
Publication statusPublished - 17 Apr 2017
Externally publishedYes


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