Exact quantum many-body scar states in the two-dimensional PXP model and their dynamical signatures

The two-dimensional PXP model is an effective model describing the dynamics of a two-dimensional Rydberg atom array in the nearest-neighbor blockade regime. We discover exponentially many exact quantum many-body scar states in the two-dimensional PXP model. These exact scar states have valence bond solid order, therefore breaking the lattice translation symmetry, despite being at effectively infinite temperature. As a manifestation of these scar states, we propose a quench experiment starting from a charge-density-wave initial state, resulting in strong oscillations in the total Rydberg-excitation number. Another signature is long-lived valence bond solid order of the scar states after a quench into a weakly perturbed model.