Two critical localization lengths in the Anderson transition on random graphs
Ignacio García-Mata, John Martin, R. Dubertrand, Olivier Giraud, Bertrand Georgeot, Gabriel Lemarié
Abstract
This paper shows that the Anderson transition on random graphs has two critical localization lengths, which control the critical behavior of specific observables, and are associated with two different critical exponents (the known ${\ensuremath{\nu}}_{\ensuremath{\parallel}}=1$ for the average localization length ${\ensuremath{\xi}}_{\ensuremath{\parallel}}$ and the new ${\ensuremath{\nu}}_{\ensuremath{\perp}}=0.5$ for the typical localization length ${\ensuremath{\xi}}_{\ensuremath{\perp}}$). The behavior we find for ${\ensuremath{\xi}}_{\ensuremath{\perp}}$ is identical to the recent predictions for the many-body localization transition, strongly suggesting that both transitions belong to the same universality class.