Anomalous diffusion and Griffiths effects near the many-body localization transition

Kartiek Agarwal, Sarang Gopalakrishnan, Michael Knap, Markus Müller, Eugene Demler

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321 Scopus citations


We explore the high-temperature dynamics of the disordered, one-dimensional XXZ model near the many-body localization (MBL) transition, focusing on the delocalized (i.e., "metallic") phase. In the vicinity of the transition, we find that this phase has the following properties: (i) local magnetization fluctuations relax subdiffusively; (ii) the ac conductivity vanishes near zero frequency as a power law; and (iii) the distribution of resistivities becomes increasingly broad at low frequencies, approaching a power law in the zero-frequency limit. We argue that these effects can be understood in a unified way if the metallic phase near the MBL transition is a quantum Griffiths phase. We establish scaling relations between the associated exponents, assuming a scaling form of the spin-diffusion propagator. A phenomenological classical resistor-capacitor model captures all the essential features.

Original languageEnglish (US)
Article number160401
JournalPhysical review letters
Issue number16
StatePublished - Apr 23 2015
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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