Exact quantum many-body scar states intrinsic to periodically driven system in the Rydberg-blockaded atom chain

In a periodically driven many-body system, any quantum state usually ends up an infinite temperature state. This is called the Floquet energy eigenstate thermalization hypothesis (Floquet ETH). Here we discuss the violation of the Floquet ETH with realistic Hamiltonians. Our periodically driven model is based on the PXP type interaction, which is demonstrated in a recent experiment in the Rydberg atoms chain by Harvard group. By showing explicit expressions of the wave functions, we exactly prove the existence of the many-body scar states, which show non-thermal behavior, while other states obey the Floquet ETH. In addition, we systematically engineer various periodically-driven Hamiltonians having Floquet many-body scar states.