Andrew Ivanov, Caltech

New rigorous insights into scars in PXP-type systems

By applying specially developed numerical techniques, we uncover previously unknown highly non-trivial exact zero-energy eigenstates hidden within the zero-energy manifolds of the non-integrable PXP-type models parametrized by the Rydberg blockade radius. We derive sufficient conditions for any matrix product state to represent an exact zero-energy eigenstate of a given one-dimensional kinetically constrained model and use them to prove the new eigenstates.

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 profound implications of these emergent exact eigenstates for the general thermalization phenomenology are exemplified by one of the states introduced in this work, which is demonstrated to be a member of the primary Z2 quantum many-body scar tower.