Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

We are pretty familiar with the phases of water: ice, liquid, and water vapor. In this talk, I discuss a quantum phase diagram of one-dimensional quantum spin system ground states with a local orthogonal group symmetry. The phases which arise in this diagram are examples of symmetry protected topological (SPT) phases of quantum matter. We will present new results on the structure of a particular family of exactly solvable models, which we call ``SO(n) Haldane Chains''. The ground states of these models exhibit a peculiar flavor of symmetry breaking and pattern of entanglement. Finally, we will compute a topological index which will allow us to confirm physical predictions that these models occupy a distinct SPT phase of matter from another well-studied class of models. 

Reception after the seminar in PSEL 2022.