Exact strong-ETH violating eigenstates and quasiparticle descriptions of many-body scar states in the Rydberg-blockaded atom chain

A recent experiment in the Rydberg atom chain observed unusual oscillatory quench dynamics with a period-2 charge density wave initial state (Z2 state), and theoretical works identified a set of many-body ``scar states'' in the Hamiltonian as potentially responsible for the atypical dynamics. In the same nonintegrable Hamiltonian, we discover several eigenstates at 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 = ± √2). This discovery explicitly demonstrates violation of strong eigenstate thermalization hypothesis in this model. These states show signatures of translational symmetry breaking with period-2 bond-centered pattern, despite being in 1d at infinite temperature. We show that the whole tower of Z2 many-body scar states can be excellently approximated as single or multiple ``quasiparticle excitations" on top of our exact E = 0 states, and propose a quasiparticle explanation of the strong oscillations observed in experiments. We also discuss the possibility of similar construction for Z3 many-body scar states relevant for quench with period-3 CDW initial state.