Two critical localization lengths in the Anderson transition on random graphs

This is the authors' abstract. We don't add key points for this paper.

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 ν_∥=1 for the average localization length ξ_∥ and the new ν_⊥=0.5 for the typical localization length ξ_⊥). The behavior we find for ξ_⊥ is identical to the recent predictions for the many-body localization transition, strongly suggesting that both transitions belong to the same universality class.