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

TL;DR

This paper investigates the dynamics near the many-body localization transition in a disordered quantum chain, revealing subdiffusive behavior, vanishing conductivity, and broad resistance distributions, all consistent with a Griffiths phase.

Contribution

It demonstrates that the metallic phase near the MBL transition exhibits Griffiths phase characteristics, unifying various anomalous transport phenomena with scaling relations.

Findings

Subdiffusive relaxation of local magnetization fluctuations

Power-law vanishing of a.c. conductivity near zero frequency

Broadening of resistance distribution approaching a power law

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 a.c. conductivity vanishes near zero frequency as a power law; (iii) the distribution of resistances 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 Griffiths phase. We establish scaling relations between the associated exponents, using exact linear-response arguments as well as a phenomenological resistor-capacitor model.