Two critical localization lengths in the Anderson transition on random graphs

@article{GarciaMata2020TwoCL,
  title={Two critical localization lengths in the Anderson transition on random graphs},
  author={Ignacio Garc'ia-Mata and J. Mart{\'i}n and R{\'e}my Dubertrand and Olivier Giraud and Bertrand Georgeot and Gabriel Lemari'e},
  journal={Physical Review Research},
  year={2020}
}
We present a full description of the nonergodic properties of wavefunctions on random graphs without boundary in the localized and critical regimes of the Anderson transition. We find that they are characterized by two localization lengths: the largest one describes localization along rare branches and diverges at the transition, while the second one describes localization along typical branches and remains finite at criticality. We show numerically that both quantities can be extracted from… 

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