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 – Published 11 April 2016

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.

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  • Received 22 January 2016

DOI:https://doi.org/10.1103/PhysRevB.93.134206

©2016 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Sarang Gopalakrishnan1, Kartiek Agarwal2, Eugene A. Demler2, David A. Huse3, and Michael Knap4

  • 1Department of Physics and Walter Burke Institute, California Institute of Technology, Pasadena, California 91125, USA
  • 2Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
  • 3Princeton University, and Institute for Advanced Study, Princeton, New Jersey 08544, USA
  • 4Department of Physics, Walter Schottky Institute, and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany

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Issue

Vol. 93, Iss. 13 — 1 April 2016

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