The PXP model describes a chain of Rydberg atoms with nearest-neighbor blockade: H = Σ P_{i-1} X_i P_{i+1}, where P=(1-|↑⟩⟨↑|)/2 is a projector onto the ground state, X is the Pauli-X operator. Excited (Rydberg) atoms cannot have adjacent neighbors.
The model is non-integrable — the bulk spectrum thermalizes (ETH, eigenstate thermalization hypothesis). Yet starting from |Z₂⟩ = |↑↓↑↓…⟩, the system shows persistent oscillations and high fidelity revivals, unlike generic initial states which quickly lose memory.
These oscillations are driven by a sparse set of quantum many-body scar states embedded in the thermal spectrum — they violate ETH. Entanglement entropy of scars grows subthermally. Discovered experimentally in 51-atom Rydberg chains (Harvard, 2017).