  The many-body localization transition is a dynamical quantum phase transition
between a localized and an extended phase. We study this transition in the XXZ
model with disordered magnetic field and focus on the time evolution following
a global quantum quench. While the dynamics of the bipartite entanglement and
spin fluctuations are already known to provide insights into the nature of the
many-body localized phases, we discuss the relevance of these quantities in the
context of the localization transition. In particular, we observe that near the
transition the long time limits of both quantities show behavior similar to
divergent thermodynamic fluctuations.
