Rare region effects and dynamics near the many-body localization transition

TL;DR

This paper reviews how rare regions influence the dynamics and properties near the many-body localization transition, affecting transport, entanglement, and phase stability.

Contribution

It synthesizes recent findings on rare-region effects in MBL systems and discusses open questions about their role in phase stability.

Findings

Rare localized regions act as transport bottlenecks.

Rare thermal regions dominate low-frequency response.

Open questions on whether a single rare thermal region can destabilize MBL.

Abstract

The low-frequency response of systems near the many-body localization phase transition, on either side of the transition, is dominated by contributions from rare regions that are locally "in the other phase", i.e., rare localized regions in a system that is typically thermal, or rare thermal regions in a system that is typically localized. Rare localized regions affect the properties of the thermal phase, especially in one dimension, by acting as bottlenecks for transport and the growth of entanglement, whereas rare thermal regions in the localized phase act as local "baths" and dominate the low-frequency response of the MBL phase. We review recent progress in understanding these rare-region effects, and discuss some of the open questions associated with them: in particular, whether and in what circumstances a single rare thermal region can destabilize the many-body localized phase.