Why the Rydberg-blockade chain shows persistent revivals
In plain words
In chains of Rydberg atoms where neighbours cannot both be excited, one special initial pattern keeps returning to itself instead of thermalizing. The underlying reason is not fully understood.
Precise statement
In the PXP model $H = \Omega \sum_i P_{i-1} X_i P_{i+1}$ (P the projector onto the atomic ground state, X the Pauli flip), the period-2 density-wave $(\mathrm{Z2})$ state shows revivals carried by a tower of special eigenstates with nearly equal energy spacing. Explain the origin of this tower (broken $\operatorname{su}(2)$ algebra, semiclassical periodic orbit, or proximity to an integrable point) in a form that predicts the revival frequency and decay rate. Answer: a theory with quantitative predictions for both.
What would settle it
A derivation predicting revival frequency and damping to within a few percent, tested against numerics at $L \ge 30$.