Unified structure for exact towers of scar states in the AKLT and other models

Understand

Quantum many-body scar states are many-body states with finite energy density in non-integrable models that do not obey the eigenstate thermalization hypothesis.

• Recent works have revealed "towers" of scar states that are exactly known and are equally spaced in energy, specifically in the AKLT model, the spin-1 XY model, and a spin-1/2 model that conserves number of domain walls.
• We provide a common framework to understand and prove known exact towers of scars in these systems, by evaluating the commutator of the Hamiltonian and a ladder operator.
• In particular we provide a simple proof of the scar towers in the integer-spin 1d AKLT models by studying two-site spin projectors.