Hypergrid subgraphs and the origin of many-body scars in constrained quantum systems

Following the recent experimental observation of wave function revivals in chains of interacting Rydberg atoms, much effort has focused on understanding the origin of many-body scars in non-integrable quantum systems. Here we argue that the many-body wave function revivals in these models stem from large hypergrid subgraphs within the adjacency graph corresponding to the quantum Hamiltonian. We explicitly identify such substructures in several constrained spin models known to host quantum many-body scars. The appearance of embedded hypergrid graphs is physically enabled by the Hilbert space constraints, and they constitute a minimal structure for an emergent su(2) spectrum-generating algebra which gives rise to quantum revivals. We illustrate our approach by providing a graph-theoretic interpretation of the Rydberg atom model, and by constructing new many-body scarred models which support robust quantum revivals from experimentally-preparable initial states.