  A recent experiment in the Rydberg atom chain observed unusual oscillatory
quench dynamics with a charge density wave initial state, and theoretical works
identified a set of many-body "scar states" showing nonthermal behavior in the
Hamiltonian as potentially responsible for the atypical dynamics. In the same
nonintegrable Hamiltonian, we discover several eigenstates at \emph{infinite
temperature} that can be represented exactly as matrix product states with
finite bond dimension, for both periodic boundary conditions (two exact $E = 0$
states) and open boundary conditions (two $E = 0$ states and one each $E = \pm
\sqrt{2}$). This discovery explicitly demonstrates violation of strong
eigenstate thermalization hypothesis in this model and uncovers exact quantum
many-body scar states. These states show signatures of translational symmetry
breaking with period-2 bond-centered pattern, despite being in one dimension at
infinite temperature. We show that the nearby many-body scar states can be well
approximated as "quasiparticle excitations" on top of our exact $E = 0$ scar
states, and propose a quasiparticle explanation of the strong oscillations
observed in experiments.
