Slow Dynamics in a Two-Dimensional Anderson-Hubbard Model

TL;DR

This paper investigates slow, subdiffusive dynamics in a two-dimensional disordered interacting system, demonstrating the effectiveness of a nonequilibrium perturbation approach and providing insights into many-body localization phenomena.

Contribution

It introduces a nonequilibrium self-consistent perturbation method that accurately captures slow dynamics in large 2D Anderson-Hubbard systems, surpassing previous computational limitations.

Findings

Strong disorder leads to nonergodic behavior.

Intermediate disorder results in subdiffusive transport.

Method aligns well with exact diagonalization for small clusters.

Abstract

We study the real-time dynamics of a two-dimensional Anderson--Hubbard model using nonequilibrium self-consistent perturbation theory within the second-Born approximation. When compared with exact diagonalization performed on small clusters, we demonstrate that for strong disorder this technique approaches the exact result on all available timescales, while for intermediate disorder, in the vicinity of the many-body localization transition, it produces quantitatively accurate results up to nontrivial times. Our method allows for the treatment of system sizes inaccessible by any numerically exact method and for the complete elimination of finite size effects for the times considered. We show that for a sufficiently strong disorder the system becomes nonergodic, while for intermediate disorder strengths and for all accessible time scales transport in the system is strictly subdiffusive. We argue that these results are incompatible with a simple percolation picture, but are consistent with the heuristic random resistor network model where subdiffusion may be observed for long times until a crossover to diffusion occurs. The prediction of slow finite-time dynamics in a two-dimensional interacting and disordered system can be directly verified in future cold atoms experiments