  We study many-body localization properties of the disordered XXZ spin chain
in the Ising phase. Disorder is introduced via a random magnetic field in the
$z$-direction. We prove a strong form of dynamical exponential clustering for
eigenstates in the droplet spectrum: For any pair of local observables
separated by a distance $\ell$, the sum of the associated correlators over
these states decays exponentially in $\ell$, in expectation. This exponential
clustering persists under the time evolution in the droplet spectrum. Our
result applies to the large disorder regime as well as to the strong Ising
phase at fixed disorder, with bounds independent of the support of the
observables.
