Subdiffusion in the Anderson model on the random regular graph

Abstract

We study the finite-Time dynamics of an initially localized wave packet in the Anderson model on the random regular graph (RRG) and show the presence of a subdiffusion phase coexisting both with ergodic and putative nonergodic phases. The full probability distribution Π(x,t) of a particle to be at some distance x from the initial state at time t is shown to spread subdiffusively over a range of disorder strengths. The comparison of this result with the dynamics of the Anderson model on Zd lattices, d>2, which is subdiffusive only at the critical point implies that the limit d→∞ is highly singular in terms of the dynamics. A detailed analysis of the propagation of Π(x,t) in space-Time (x,t) domain identifies four different regimes determined by the position of a wave front Xfront(t), which moves subdiffusively to the most distant sites Xfront(t)∼tβ with an exponent β<1. Importantly, the Anderson model on the RRG can be considered as proxy of the many-body localization transition (MBL) on the Fock space of a generic interacting system. In the final discussion, we outline possible implications of our findings for MBL.