  Recent experiments on Rydberg atom arrays have found evidence of anomalously
slow thermalization and persistent density oscillations, which have been
interpreted as a many-body analog of the phenomenon of quantum scars. Periodic
dynamics and atypical scarred eigenstates originate from a "hard" kinetic
constraint: the neighboring Rydberg atoms cannot be simultaneously excited.
Here we propose a realization of quantum many-body scars in a 1D bosonic
lattice model with a "soft" constraint in the form of density-assisted hopping.
We discuss the relation of this model to the standard Bose-Hubbard model and
possible experimental realizations using ultracold atoms. We find that this
model exhibits similar phenomenology to the Rydberg atom chain, including
weakly entangled eigenstates at high energy densities and the presence of a
large number of exact zero energy states, with distinct algebraic structure.
