TY - JOUR
T1 - Griffiths effects and slow dynamics in nearly many-body localized systems
AU - Gopalakrishnan, Sarang
AU - Agarwal, Kartiek
AU - Demler, Eugene A.
AU - Huse, David A.
AU - Knap, Michael
N1 - Funding Information:
We thank E. Altman, F. Huveneers, M. Muller, A. Potter, U. Schneider, and especially V. Oganesyan for helpful discussions. The authors acknowledge support from Harvard-MIT CUA, NSF Grant No. DMR-1308435, AFOSR Quantum Simulation MURI, the ARO-MURI on Atomtronics, ARO MURI Quism program. S.G. acknowledges support from the Walter Burke Institute at Caltech and from the National Science Foundation under Grant No. NSF PHY11-25915. D.A.H. is the Addie and Harold Broitman Member at I.A.S. M.K. acknowledges support from Technical University of Munich - Institute for Advanced Study, funded by the German Excellence Initiative and the European Union FP7 under grant agreement 291763. E.D. acknowledges support from the Humboldt Foundation, Dr. Max Rassler, the Walter Haefner Foundation, and the ETH Foundation.
Publisher Copyright:
© 2016 American Physical Society.
PY - 2016/4/11
Y1 - 2016/4/11
N2 - 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.
AB - 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.
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U2 - 10.1103/PhysRevB.93.134206
DO - 10.1103/PhysRevB.93.134206
M3 - Article
AN - SCOPUS:84963620818
SN - 2469-9950
VL - 93
JO - Physical Review B
JF - Physical Review B
IS - 13
M1 - 134206
ER -