Many exact area-law scar eigenstates in the nonintegrable PXP and related models

In this work, we present new, highly non-trivial area-law exact zero-energy eigenstates of the one-dimensional (1D) PXP and related models. We formulate sufficient conditions for a matrix product state to represent an exact zero-energy eigenstate of a given 1D kinetically constrained model and use them to prove our new states. We also demonstrate that all previously known exact eigenstates of PXP-type models satisfy these conditions, and, in fact, can be directly deduced from them. We discuss and demonstrate a remarkably effective general numerical technique for discovering finite-bond-dimension eigenstates residing in degenerate subspaces of a broad class of Hamiltonians. Our results highlight a previously unrecognized structure characteristic of the exponentially large nullspaces in kinetically constrained models, suggesting the possibly of extensively many increasingly complex area-law zero-energy eigenstates in the thermodynamic limit. The important implications of these emergent exact eigenstates for the general thermalization phenomenology are exemplified by one of the states introduced in this work, which we propose is a member of the primary $\mathbb{Z}_2$ quantum many-body scar tower responsible for long-lived revivals in the Rydberg atom chain experiment.