  Due to a phenomenon of many-body localization (MBL), the strong disorder may
significantly slow down or even completely hinder the thermalization of quantum
many-body systems. A sufficiently deep quasiperiodic potential may also inhibit
thermalization. In this work, we numerically demonstrate direct differences in
the behavior of standard ergodicity-breaking indicators at the MBL crossover in
random and quasiperiodic systems. Our key finding is the exponential increase
in the sharpness of the MBL crossover with system size for quasiperiodic
systems, a trend that is only linear in disordered systems. The strong tendency
towards a non-analytic behavior in quasiperiodic systems is consistent with the
existence of dynamical regimes with sharply defined boundaries or an MBL phase
transition. It highlights the importance of quasiperiodic systems for our
understanding of many-body dynamics.
