  In the presence of sufficiently strong disorder or quasiperiodic fields, an
interacting many-body system can fail to thermalize and become many-body
localized. The associated transition is of particular interest, since it occurs
not only in the ground state but over an extended range of energy densities. So
far, theoretical studies of the transition have focused mainly on the case of
true-random disorder. In this work, we experimentally and numerically
investigate the regime close to the many-body localization transition in
quasiperiodic systems. We find slow relaxation of the density imbalance close
to the transition, strikingly similar to the behavior near the transition in
true-random systems. This dynamics is found to continuously slow down upon
approaching the transition and allows for an estimate of the transition point.
We discuss possible microscopic origins of these slow dynamics.
