Dynamics of antiferromagnetic dimers in Rydberg atom chains

We investigate the dynamics of antiferromagnetic dimers within a Rydberg atom chain in the regime where laser detuning compensates for nearest-neighbor (NN) interactions. Using an effective PXQ model, we demonstrate that the associated Hilbert space decomposes into disconnected dimer-conserving subspaces. The classification of these subspaces is provided, and the computational basis states spanning them are identified. Through a combination of analytical mapping and numerical simulations, we compare the dynamics of the PXQ model with those of the full Rydberg atom chain. The deviations are attributed to two factors: laser-induced leakage from the constrained Hilbert subspace and the influence of long-range interactions beyond the NN limit. Our results indicate that subspace leakage can be mitigated by increasing the NN interaction strength. While this simultaneously amplifies the effects of long-range interactions, the conservation of the dimer number remains. Our study opens up possibilities for exploring the dynamics of antiferromagnetic dimers using the Rydberg atom quantum simulator.