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

Gopalakrishnan, Sarang and Agarwal, Kartiek and Demler, Eugene A. and Huse, David A. and Knap, Michael (2016) Griffiths effects and slow dynamics in nearly many-body localized systems. Physical Review B, 93 (13). Art. No. 134206. ISSN 2469-9950. doi:10.1103/PhysRevB.93.134206.

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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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Additional Information:© 2016 American Physical Society. Received 22 January 2016; published 11 April 2016. We thank E. Altman, F. Huveneers, M. Müller, 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 Rössler, the Walter Haefner Foundation, and the ETH Foundation.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)UNSPECIFIED
Army Research Office (ARO)UNSPECIFIED
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Technical University of MunichUNSPECIFIED
Deutsche Forschungsgemeinschaft (DFG)UNSPECIFIED
European Union FP7291763
Alexander von Humboldt FoundationUNSPECIFIED
Walter Haefner FoundationUNSPECIFIED
Issue or Number:13
Record Number:CaltechAUTHORS:20160429-104643765
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Official Citation:Griffiths effects and slow dynamics in nearly many-body localized systems Sarang Gopalakrishnan, Kartiek Agarwal, Eugene A. Demler, David A. Huse, and Michael Knap Phys. Rev. B 93, 134206
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:66550
Deposited By: Tony Diaz
Deposited On:29 Apr 2016 19:24
Last Modified:10 Nov 2021 23:59

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