  Emerging dynamical constraints resulting from inter-site interactions
severely limit particle mobility in polar lattice gases. Whereas in absence of
disorder hard-core Hubbard models with only strong nearest-neighbor
interactions present Hilbert space fragmentation but no many-body localization
for typical states, the $1/r^3$ tail of the dipolar interaction results in
Hilbert space shattering, as well as in a dramatically slowed down dynamics and
eventual disorder-free localization. Our results show that the study of the
intriguing interplay between disorder- and interaction-induced many-body
localization is within reach of future experiments with magnetic atoms and
polar molecules.
