Topological universality class and spin dynamics of n-fold symmetric magnetic molecules

The low energy spin dynamics of many n-fold symmetric magnetic molecules for n ≥ 3 can be effectively described by an infinite range, XXZ Heisenberg model in the presence of an external magnetic field. Employing the topological classification scheme for the unitary flag manifold, we establish the topological universality class of the Hilbert space for such effective models. We elucidate the emergent symmetries at the field induced level crossings (or Weyl points) and their implications for the spin dynamics. We also address the topological universality classes of closely related U(1) symmetric Lipkin Meshkov Glick model and Tavis Cummings model.