  Recent theoretical and numerical evidence suggests that localization can
survive in disordered many-body systems with very high energy density, provided
that interactions are sufficiently weak. Stronger interactions can destroy
localization, leading to a so-called many-body localization transition. This
dynamical phase transition is relevant to questions of thermalization in
extended quantum systems far from the zero-temperature limit. It separates a
many-body localized phase, in which localization prevents transport and
thermalization, from a conducting ("ergodic") phase in which the usual
assumptions of quantum statistical mechanics hold. Here, we present numerical
evidence that many-body localization also occurs in models without disorder but
rather a quasiperiodic potential. In one dimension, these systems already have
a single-particle localization transition, and we show that this transition
becomes a many-body localization transition upon the introduction of
interactions. We also comment on possible relevance of our results to
experimental studies of many-body dynamics of cold atoms and non-linear light
in quasiperiodic potentials.
