Topological many-body scar states in dimensions one, two, and three

We propose an exact construction for atypical excited states of a class of nonintegrable quantum many-body Hamiltonians in one, two, and three dimensions that display area-law entanglement entropy. These examples of many-body "scar" states have, by design, other properties, such as topological degeneracies, usually associated with the gapped ground states of symmetry-protected topological phases or topologically ordered phases of matter.