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

• Published in: Annalen der Physik 2017-07, Vol.529 (7), p.n/a
• Main Authors: Agarwal, Kartiek, Altman, Ehud, Demler, Eugene, Gopalakrishnan, Sarang, Huse, David A., Knap, Michael
• Format: Article
• Language: English
• Subjects: Dynamical systems; Entanglement; Frequency response; Griffiths effects; Localization; localization physics; Phase transitions; slow dynamical phenomena
• ISSN: 0003-3804; 1521-3889
• DOI: 10.1002/andp.201600326

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. The many‐body localization transition demarcates quantum phases of matter that are remarkably different in their entanglement structure, response, and dynamical properties. Near the transition, this difference plays a significant role as rare inclusions of the opposite phase strongly modify the properties of the bulk, ‘enabling’ the transition, but also giving rise to a new ‘Griffiths’ phase with entirely novel dynamical characteristics. This review reflects the current understanding of such ‘Griffiths’ effects on the many‐body localization transition.