Agarwal, KartiekGopalakrishnan, SarangKnap, MichaelMüller, MarkusDemler, Eugene2019-09-262015Agarwal, Kartiek, Sarang Gopalakrishnan, Michael Knap, Markus Müller, and Eugene Demler. 2015. “Anomalous Diffusion and Griffiths Effects Near the Many-Body Localization Transition.” Physical Review Letters 114 (16). https://doi.org/10.1103/physrevlett.114.160401.0031-90071079-71141092-0145http://nrs.harvard.edu/urn-3:HUL.InstRepos:41412205We 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.en-USJournal Article2019-09-2610.1103/PhysRevLett.114.160401