| Issue |
EPL
Volume 144, Number 4, November 2023
|
|
|---|---|---|
| Article Number | 41001 | |
| Number of page(s) | 6 | |
| Section | Statistical physics and networks | |
| DOI | https://doi.org/10.1209/0295-5075/ad1001 | |
| Published online | 11 December 2023 | |
Multifractality and statistical localization in highly heterogeneous random networks
1 Institute for Theoretical Physics, Georg-August-Universität Göttingen - 37077 Göttingen, Germany
2 Department of Mathematics, King's College London - London WC2R 2LS, UK
Received: 23 August 2023
Accepted: 27 November 2023
We consider highly heterogeneous random networks with symmetric interactions in the limit of high connectivity. A key feature of this system is that the spectral density of the corresponding ensemble exhibits a divergence within the bulk. We study the structure of the eigenvectors associated with this divergence and find that they are multifractal with the statistics of eigenvector elements matching those of the resolvent entries. The corresponding localization mechanism relies on the statistical properties of the nodes rather than on any spatial structure around a localization centre. This “statistical localization” mechanism is potentially relevant for explaining localization in different models that display singularities in the bulk of the spectrum of eigenvalues.
© 2023 The author(s)
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