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

Author(s): Gopalakrishnan, Sarang; Agarwal, Kartiek; Demler, Eugene A; Huse, David A; Knap, Michael

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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 dc 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 wave-vector-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.
Publication Date: Apr-2016
Electronic Publication Date: 11-Apr-2016
Citation: Gopalakrishnan, Sarang, Agarwal, Kartiek, Demler, Eugene A, Huse, David A, Knap, Michael. (2016). Griffiths effects and slow dynamics in nearly many-body localized systems. Physical Review B, 93 (13), 10.1103/PhysRevB.93.134206
DOI: doi:10.1103/PhysRevB.93.134206
ISSN: 2469-9950
EISSN: 2469-9969
Type of Material: Journal Article
Journal/Proceeding Title: Physical Review B
Version: Author's manuscript

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