Dynamics of entanglement and transport in one-dimensional systems with quenched randomness

The thermalization of one-dimensional quantum systems may be severely slowed by weak links, e.g., by the Griffiths regions that dominate the long-time dynamics of a system close to the many-body-localization transition. Here, the authors construct universal coarse-grained descriptions for entanglement production and for the dynamics of quantum operators in systems with weak links. They reveal unexpected differences between these processes (for example, entanglement growth can be slower than linear in time even when operators spread ballistically). The universal physics is explained using simple classical effective models. The authors' analysis of the spreading of quantum information and of conserved quantities shows that thermalization in the presence of weak links has a rich structure, featuring multiple dynamic length scales that diverge with different powers of time.