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

TL;DR

This paper analyzes Griffiths effects and slow dynamics near the many-body localization transition, showing how rare regions influence low-frequency response and long-time behavior in various dimensions.

Contribution

It provides a comprehensive analysis of Griffiths effects in the thermal phase near the MBL transition across different dimensions and systems, including linear response and dynamics.

Findings

Rare regions dominate low-frequency response near MBL transition

Long-time local observables can be governed by Griffiths effects in 1D and Floquet systems

Hydrodynamic tails often dominate generic observables in the thermal phase

Abstract

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. In all the regimes we consider, we identify observables that are dominated by rare-region effects. In some cases (one-dimensional systems and Floquet systems with no extensive conserved quantities), essentially all long-time local observables are dominated by rare-region effects; in others, generic observables are instead dominated by hydrodynamic long-time tails throughout the thermal phase, and one must look at specific probes, such as spin echo, to see Griffiths behavior.