Anomalous Diffusion and Griffiths Effects Near the Many-Body Localization Transition

TLDR

The study investigates high‑temperature dynamics of the disordered one‑dimensional XXZ model near the many‑body localization transition, concentrating on the delocalized (metallic) phase. The authors derive scaling relations for spin‑diffusion exponents and employ a phenomenological classical resistor‑capacitor model to capture the observed dynamical behavior. They find that close to the transition the metallic phase displays subdiffusive magnetization relaxation, a power‑law suppression of low‑frequency ac conductivity, and a broadening resistivity distribution that converges to a power law, all of which are characteristic of a quantum Griffiths phase.

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.