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Journal Article

Subdiffusion in the Anderson model on the random regular graph


Khaymovich,  Ivan M.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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De Tomasi, G., Bera, S., Scardicchio, A., & Khaymovich, I. M. (2020). Subdiffusion in the Anderson model on the random regular graph. Physical Review B, 101(10): 100201. doi:10.1103/PhysRevB.101.100201.

Cite as: https://hdl.handle.net/21.11116/0000-0006-3F0B-9
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 Pi(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) lattices, d > 2, which is subdiffusive only at the critical point implies that the limit d -> infinity is highly singular in terms of the dynamics. A detailed analysis of the propagation of Pi(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) similar to t(beta) with an exponent beta < 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.