paper

Dynamics of Many-Body Delocalization in the Time-dependent Hartree-Fock Approximation

arXiv:2101.07018 · doi:10.1016/j.aop.2021.168486

Abstract

We explore dynamics of disordered and quasi-periodic interacting lattice models using a self-consistent time-dependent Hartree-Fock (TDHF) approximation, accessing both large systems (up to sites) and very long times (up to ). We find that, in the limit, the many-body localization (MBL) is always destroyed within the TDHF approximation. At the same time, this approximation provides important information on the long-time character of dynamics in the ergodic side of the MBL transition. Specifically, for one-dimensional (1D) disordered chains, we find slow power-law transport up to the longest times, supporting the rare-region (Griffiths) picture. The information on this subdiffusive dynamics is obtained by the analysis of three different observables - temporal decay of real-space and energy-space imbalances as well as domain wall melting - which all yield consistent results. For two-dimensional (2D) systems, the decay is faster than a power law, in consistency with theoretical predictions that grows as for the decay governed by rare regions. At longest times and moderately strong disorder, approaches the limiting value corresponding to 2D diffusion. In quasi-periodic (Aubry-André) 1D systems, where rare regions are absent, we find considerably faster decay that reaches the ballistic value , which provides further support to the Griffiths picture of the slow transport in random systems.

arXiv comment35 pages including appendix, 14 figures. Comments welcome

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