Disorder enhanced quantum many-body scars in Hilbert hypercubes

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, 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.