title: Anomalous diffusion and griffiths effects near the many-body localization transition.
abstract: 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.
authors.affiliation: Physics Department, Harvard University, Cambridge, Massachusetts 02138, USA.
authors.forename: Kartiek
authors.initials: K
authors.lastname: Agarwal
authors.affiliation: Physics Department, Harvard University, Cambridge, Massachusetts 02138, USA.
authors.forename: Sarang
authors.initials: S
authors.lastname: Gopalakrishnan
authors.affiliation: Physics Department, Harvard University, Cambridge, Massachusetts 02138, USA.|ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA.
authors.forename: Michael
authors.initials: M
authors.lastname: Knap
authors.affiliation: The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy.|Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland.
authors.forename: Markus
authors.initials: M
authors.lastname: Müller
authors.affiliation: Physics Department, Harvard University, Cambridge, Massachusetts 02138, USA.
authors.forename: Eugene
authors.initials: E
authors.lastname: Demler