Quantum scars as embeddings of weakly "broken" Lie algebra representations

Understand

We present an interpretation of scar states and quantum revivals as weakly "broken" representations of Lie algebras spanned by a subset of eigenstates of a many-body quantum system.

• We show that the PXP model, describing strongly-interacting Rydberg atoms, supports a "loose" embedding of multiple $\mathrm{su(2)}$ Lie algebras corresponding to distinct families of scarred eigenstates.
• Moreover, we demonstrate that these embeddings can be made progressively more accurate via an iterative process which results in optimal perturbations that stabilize revivals from arbitrary charge density wave product states, $|\mathbb{Z}_n\rangle$, including ones that show no revivals in the unperturbed PXP model.
• We discuss the relation between the loose embeddings of Lie algebras present in the PXP model and recent exact constructions of scarred states in related models.