Disorder enhanced quantum many-body scars in Hilbert hypercubes

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