  One fundamental assumption in statistical physics is that generic closed
quantum many-body systems thermalize under their own dynamics. Recently, the
emergence of many-body localized systems has questioned this concept,
challenging our understanding of the connection between statistical physics and
quantum mechanics. Here we report on the observation of a many-body
localization transition between thermal and localized phases for bosons in a
two-dimensional disordered optical lattice. With our single site resolved
measurements we track the relaxation dynamics of an initially prepared
out-of-equilibrium density pattern and find strong evidence for a diverging
length scale when approaching the localization transition. Our experiments mark
the first demonstration and in-depth characterization of many-body localization
in a regime not accessible with state-of-the-art simulations on classical
computers.
