Griffiths effects and slow dynamics in nearly many-body localized systems

Understand

The low-frequency response of systems near a many-body localization transition can be dominated by rare regions that are locally critical or "in the other phase".

• It is known that, in one dimension, these rare regions can cause the d.c.
• conductivity and diffusion constant to vanish even inside the delocalized thermal phase.
• Here, we present a general analysis of such Griffiths effects in the thermal phase near the many-body localization transition: we consider both one-dimensional and higher-dimensional systems, subject to quenched randomness, and discuss both linear response (including the frequency- and wavevector-dependent conductivity) and more general dynamics.