Strong Quantum Mpemba Effect from Exact Slow-Mode Selection in Constrained Rydberg Chains

Can a many-body state relax faster because it is blind to the slowest decay channel? We show that this mechanism gives rise to a robust strong quantum Mpemba effect in locally dephased constrained Rydberg chains. The key observation is that, for constrained single-spin-flip Hamiltonians, local dephasing turns the Hamiltonian itself into an exact left Liouvillian slow mode, mathcal L^dagger(H)=-γH. A thermal state generically retains this slow channel, whereas translationally invariant states with vanishing energy expectation remove it and are forced to relax through faster visible modes. This exact selection rule produces a strong quantum Mpemba effect in the locally dephased PXP chain, including for a zero-energy scar eigenstate, the |0cdots0rangle product state, and a translation-invariant Z₂ cat state. We further show that the same mechanism persists in the (2,3) model and in the longer-range blockade family. Our results identify exact slow-mode selection, rather than special scar wave functions, as a general organizing principle for anomalously fast relaxation in constrained open quantum systems.