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Following the recent observation of wave function revivals in large Rydbergatom quantum simulators, much effort has focused on understanding the emergenceof many-body scars in non-integrable quantum systems. Here we explore theorigin of scarred wavefunction revivals in a family of models obtained bydeforming the graph adjacency matrix of the PXP model - the effective model ofRydberg atoms in the strong Rydberg blockade regime. We consider deformationsthat either enhance the Rydberg constraint, ultimately resulting in aneffective tight-binding model of two hypercubes joined at a single vertex, orrelax the constraint until reaching the free spin-1/2 model. In the formercase, we argue that the model of two joined hypercubes captures the essentialfeatures of many-body scarring present in the PXP model. On the other hand,relaxing the constraint leads to a sequence of new scarred models, some withmore robust scarring signatures than the PXP model, as can be understood fromthe graph-theoretic viewpoint. Our results shed light on the nature of scarringin the PXP model by identifying its simple parent model, while alsohighlighting its distinction from the free-spin precession.

Hypergrid subgraphs and the origin of scarred quantum walks in the many-body Hilbert space