Article (Scientific journals)
Scaling Theory of the Anderson Transition in Random Graphs: Ergodicity and Universality
Garcia-Mata, Ignacio; Giraud, Olivier; Georgeot, Bertrand et al.
2017In Physical Review Letters, 118, p. 166801
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Abstract :
[en] 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.
Research center :
CESAM - Complex and Entangled Systems from Atoms to Materials - ULiège
Disciplines :
Physics
Author, co-author :
Garcia-Mata, Ignacio
Giraud, Olivier
Georgeot, Bertrand
Martin, John  ;  Université de Liège > Département de physique > Optique quantique
Dubertrand, Rémy ;  Université de Liège > Département de physique > Optique quantique
Lemarié, Gabriel
Language :
English
Title :
Scaling Theory of the Anderson Transition in Random Graphs: Ergodicity and Universality
Publication date :
17 April 2017
Journal title :
Physical Review Letters
ISSN :
0031-9007
eISSN :
1079-7114
Publisher :
American Physical Society, Ridge, United States - New York
Volume :
118
Pages :
166801
Peer reviewed :
Peer Reviewed verified by ORBi
Tags :
CÉCI : Consortium des Équipements de Calcul Intensif
Funders :
CÉCI - Consortium des Équipements de Calcul Intensif [BE]
Available on ORBi :
since 18 April 2017

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