Universality in Anderson localization on random graphs with varying connectivity
Piotr Sierant, Maciej Lewenstein, Antonello Scardicchio
SciPost Phys. 15, 045 (2023) · published 3 August 2023
- doi: 10.21468/SciPostPhys.15.2.045
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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 $W_{E}$ which is strictly less than the Anderson localization critical disorder $W_C$, and that of other works which suggest that there is no such region. We find that, although no separate $W_{E}$ exists from $W_C$, the length scale at which fully developed ergodicity is found diverges like $|W-W_C|^{-1}$, while the critical length over which delocalization develops is $\sim |W-W_C|^{-1/2}$. 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.
Cited by 19
Authors / Affiliations: mappings to Contributors and Organizations
See all Organizations.- 1 Piotr Sierant,
- 1 2 Maciej Lewenstein,
- 3 4 Antonello Scardicchio
- 1 Institut de Ciències Fotòniques / Institute of Photonic Sciences [ICFO]
- 2 Institució Catalana de Recerca i Estudis Avançats [ICREA]
- 3 Centro Internazionale di Fisica Teorica Abdus Salam / Abdus Salam International Centre for Theoretical Physics [ICTP]
- 4 INFN Sezione di Trieste / INFN Trieste
- European Commission [EC]
- European Research Council [ERC]
- FUNDACIÓ Privada MIR-PUIG
- Fundacion Cellex (through Organization: Fundació Privada Cellex)
- Generalitat de Catalunya / Government of Catalonia
- HORIZON EUROPE Framework Programme
- Horizon 2020 (through Organization: European Commission [EC])
- Institut de Ciències Fotòniques / Institute of Photonic Sciences [ICFO]
- Ministerio de Ciencia e Innovación
- Ministerio de Economía y Competitividad (MINECO) (through Organization: Ministerio de Economía, Industria y Competitividad / Ministry of Economy, Industry and Competitiveness [MINECO])
- Ministero dell'Università e della Ricerca
- Narodowe Centrum Nauki / National Science Center [NCN]
- “la Caixa” Foundation