Subdiffusion in the Anderson model on the random regular graph

Giuseppe De Tomasi, Soumya Bera, Antonello Scardicchio, Ivan M. Khaymovich
2020 Physical review B  
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 (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 Z d
more » ... on model on Z d 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 (x, t ) in space-time (x, t ) domain identifies four different regimes determined by the position of a wave front X front (t ), which moves subdiffusively to the most distant sites X front (t ) ∼ t β 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.
doi:10.1103/physrevb.101.100201 fatcat:drnyq4lxxngthcs3fypgin4vnu