  Understanding the dynamics of strongly interacting disordered quantum systems
is one of the most challenging problems in modern science, due to features such
as the breakdown of thermalization and the emergence of glassy phases of
matter. We report on the observation of anomalous relaxation dynamics in an
isolated XXZ quantum spin system realized by an ultracold gas of atoms
initially prepared in a superposition of two-different Rydberg states. The
total magnetization is found to exhibit sub-exponential relaxation analogous to
classical glassy dynamics, but in the quantum case this relaxation originates
from the build-up of non-classical correlations. In both experiment and
semi-classical simulations, we find the evolution towards a randomized state is
independent of the strength of disorder up to a critical value. This hints
towards a unifying description of relaxation dynamics in disordered isolated
quantum systems, analogous to the generalization of statistical mechanics to
out-of-equilibrium scenarios in classical spin glasses.
