Journal
PHYSICAL REVIEW B
Volume 93, Issue 13, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.93.134206
Keywords
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Funding
- Harvard-MIT CUA
- NSF Grant [DMR-1308435]
- AFOSR Quantum Simulation MURI
- ARO-MURI on Atomtronics
- ARO MURI Quism program
- Walter Burke Institute at Caltech
- National Science Foundation [NSF PHY11-25915]
- Technical University of Munich - Institute for Advanced Study
- German Excellence Initiative
- European Union FP7 [291763]
- Humboldt Foundation
- Walter Haefner Foundation
- ETH Foundation
- Direct For Mathematical & Physical Scien
- Division Of Materials Research [1308435] Funding Source: National Science Foundation
- Direct For Mathematical & Physical Scien
- Division Of Physics [1205923] Funding Source: National Science Foundation
- Division Of Physics
- Direct For Mathematical & Physical Scien [1205635] Funding Source: National Science Foundation
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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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