2012/11/30 by Giulio Biroli, Biroli, G., Ana C. Ribeiro-Teixeira +3 · 1 citation
Engineering · Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Organic Light-Emitting Diodes Research #Quantum Physics (quant-ph) #Quantum and electron transport phenomena #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1211.7334
openalex publication_date 2012/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We show that non-interacting disordered electrons on a Bethe lattice display a new intermediate phase which is delocalized but non-ergodic, i.e. it is characterized by Poisson instead of GOE statistics. The physical signature of this phase is a very heterogenous transport that proceeds over a few disorder dependent paths only. We show that the transition to the usual ergodic delocalized phase, which takes place for a disorder strength smaller than the one leading to the localization transition, is related to the freezing-glass transition of directed polymers in random media. The numerical study of level and eigenstate statistics, and of the singular properties of the probability distribution of the local density of states all support the existence of this new intermediate phase. Our results suggest that the localization transition may change nature in high dimensional systems.