Sub-diffusion in the Anderson model on random regular graph

Giuseppe De Tomasi; Soumya Bera; Antonello Scardicchio; Ivan M. Khaymovich

doi:10.1103/PhysRevB.101.100201

paper

Sub-diffusion in the Anderson model on random regular graph

arXiv:1908.11388 · doi:10.1103/PhysRevB.101.100201

Abstract

We study the finite-time dynamics of an initially localized wave-packet in the Anderson model on the random regular graph (RRG). Considering the full probability distribution $Π (x, t)$ of a particle to be at some distance $x$ from the initial state at time $t$ , we give evidence that $Π (x, t)$ spreads sub-diffusively over a range of disorder strengths, wider than a putative non-ergodic phase. We provide a detailed analysis of the propagation of $Π (x, t)$ in space-time $(x, t)$ domain, identifying four different regimes. These regimes in $(x, t)$ are determined by the position of a wave-front $X_{front} (t)$ , which moves sub-diffusively to the most distant sites $X_{front} (t) \sim t^{β}$ with an exponent $β < 1$ . We support our numerical results by a self-consistent semiclassical picture of wavepacket propagation relating the exponent $β$ with the relaxation rate of the return probability $Π (0, t) \sim e^{- Γ t^{β}}$ . 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.

arXiv comment7 pages, 5 figures, 90 references + 4 pages, 8 figures in appendices

Sub-diffusion in the Anderson model on random regular graph

Abstract

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