Affiliation:
1. Institute of Photonic Sciences
2. Institució Catalana de Recerca i Estudis Avançats
3. Abdus Salam International Centre for Theoretical Physics
4. INFN Trieste
Abstract
We perform a thorough and complete analysis of the Anderson localization transition on several models of random graphs with regular and random connectivity. The unprecedented precision and abundance of our exact diagonalization data (both spectra and eigenstates), together with new finite size scaling and statistical analysis of the graph ensembles, unveils a universal behavior which is described by two simple, integer, scaling exponents. A by-product of such analysis is a reconciliation of the tension between the results of perturbation theory coming from strong disorder and earlier numerical works, which seemed to suggest that there should be a non-ergodic region above a given value of disorder W_{E}WE which is strictly less than the Anderson localization critical disorder W_CWC, and that of other works which suggest that there is no such region. We find that, although no separate W_{E}WE exists from W_CWC, the length scale at which fully developed ergodicity is found diverges like |W-W_C|^{-1}|W−WC|−1, while the critical length over which delocalization develops is \sim |W-W_C|^{-1/2}∼|W−WC|−1/2. The separation of these two scales at the critical point allows for a true non-ergodic, delocalized region. In addition, by looking at eigenstates and studying leading and sub-leading terms in system size-dependence of participation entropies, we show that the former contain information about the non-ergodicity volume which becomes non-trivial already deep in the delocalized regime. We also discuss the quantitative similarities between the Anderson transition on random graphs and many-body localization transition.
Funder
European Commission
European Research Council
FUNDACIÓ Privada MIR-PUIG
Fundacion Cellex
Generalitat de Catalunya
HORIZON EUROPE Framework Programme
Horizon 2020
Institut de Ciències Fotòniques
Ministerio de Ciencia e Innovación
Ministerio de Economía y Competitividad
Ministero dell'Università e della Ricerca
Narodowe Centrum Nauki
“la Caixa” Foundation
Subject
General Physics and Astronomy
Cited by
4 articles.
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