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 of a particle to be at some distance from the initial state at time is shown to spread subdiffusively over a range of disorder strengths. The comparison of this result with the dynamics of the Anderson model on lattices, , which is subdiffusive only at the critical point implies that the limit is highly singular in terms of the dynamics. A detailed analysis of the propagation of in space-time domain identifies four different regimes determined by the position of a wave front , which moves subdiffusively to the most distant sites with an exponent . 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.
- Received 11 September 2019
- Revised 20 December 2019
- Accepted 10 January 2020
DOI:https://doi.org/10.1103/PhysRevB.101.100201
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.
Published by the American Physical Society