Fractionalization paves the way to local projector embeddings of quantum many-body scars

Many systems that host exact quantum many-body scars (towers of energy-equidistant low entanglement eigenstates) are governed by a Hamiltonian that splits into a Zeeman term and a sum of local terms that annihilate the scar subspace. We show that this unifying structure also applies to models, such as the Affleck-Kennedy-Lieb-Tasaki (AKLT) model or the PXP model of Rydberg-blockaded atoms, that were previously believed to evade this characterisation. To fit these models within the local annihilator framework we need to fractionalize their degrees of freedom and enlarge the associated Hilbert space. The embedding of the original system in a larger space elucidates the structure of their scar states and simplifies their construction, revealing close analogies with lattice gauge theories.