  The isolated one-dimensional Heisenberg model with static random magnetic
fields has become paradigmatic for the analysis of many-body localization.
Here, we study the dynamics of this system initially prepared in a
highly-excited nonstationary state. Our focus is on the probability for finding
the initial state later in time, the so-called survival probability. Two
distinct behaviors are identified before equilibration. At short times, the
decay is very fast and equivalent to that of clean systems. It subsequently
slows down and develops a powerlaw behavior with an exponent that coincides
with the multifractal dimension of the eigenstates.
