  We study a model of Rydberg atoms in a nearest-neighbor Rydberg blockaded
regime, introduced by Lesanovsky in Phys. Rev. Lett. 108, 105301 (2012). This
many-body model (which has one parameter $z$) has an exactly known gapped
liquid ground state, and two exactly known low-lying excitations. We discover
two new exact low-lying eigenstates. We also discuss behavior of the model at
small parameter $z$ and its proximity to an integrable model. Lastly, we
discuss connections between the Lesanovsky model at intermediate $z$ and
so-called PXP model. The PXP model describes a recent experiment that observed
unusual revivals from a charge density wave initial state, which are attributed
to a set of many-body "scar states" which do not obey the eigenstate
thermalization hypothesis. We discuss the possibility of scar states in the
Lesanovsky model and present two approximations for them.
