Topological universality class and spin dynamics of Fe₈ model and significant others

The low-energy spin dynamics of 2-fold symmetric magnetic molecules like Fe₈ can be effectively described by an infinite range, XYZ 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 quantum Rabi and quantum Dicke models.