  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.
