Hopfions in lattice dimer model

In this talk I consider hopfions in 3D lattice dimer model, i.e. topological defects, which can be characterized by 3D topological Hopf invariant. More specifically, I consider 3D bipartite lattice dimer model, define its configurations as equivalent if they can be transformed into each other by a set of local flips, and derive, that they preserve Hopf number. In this way, Hopf invariants answer the question of ergodicity in bipartite lattice dimer model. Furthermore, I consider the case of non-bipartite lattice dimer model, and by using neural networks, demonstrate that its topological phases are characterized by Z2 topological invariant. Since the lattice dimer model is known to describe classical spin ice, my work can be viewed as a proposal to search for hopfions in spin ice materials.