We consider a model arising in facilitated Rydberg chains with positional disorder which features a Hilbert space with the topology of a $d$-dimensional hypercube. This allows for a straightforward interpretation of the many-body dynamics in terms of a single-particle one on the Hilbert space and provides an explicit link between the many-body and single-particle scars. Exploiting this perspective, we show that an integrability-breaking disorder enhances the scars followed by inhibition of the dynamics due to strong localization of the eigenstates in the large disorder limit. Next, mapping the model to the spin-1/2 XX Heisenberg chain offers a simple geometrical perspective on the recently proposed Onsager scars [Phys. Rev. Lett. 124, 180604 (2020)], which can be identified with the scars on the edge of the Hilbert space. This makes apparent the origin of their insensitivity to certain types of disorder perturbations.

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• Cold gases in optical lattices
• Nonequilibrium statistical mechanics
• Quantum quench
• Quantum scars
• Spin dynamics
• 1-dimensional spin chains
• Disordered systems
• Rydberg atoms & molecules
• Quantum spin chains