Exact (ground) states and zero-modes of interacting Spin and Clock models

In this talk, I will first review the old results of Peschel and Emery, who devised a set of interacting spin-1/2 models, for which the degenerate ground states can be written in terms of product states. This model has more interesting properties, such as excited states that can be constructed explicitly, and one can find exact, local operators that swap the ground states. These results can be generalized to three state Clock models, and models with arbitrary spin. If time allows, I will comment on how to adapt the construction to arbitrary lattices. This talk will have substantial overlap with Iman Mahyaeh’s licentiate defense.