Title: Exactly solvable models of topological matter in 3D

Abstract:

There are still open questions surrounding the kinds of topological and symmetry protected states of matter that exist in 3D. It therefore makes sense to investigate solvable models in 3D exhibiting topological behaviour, and understand their properties. In this work we study such a class of exactly solvable spin models, first put forward by Walker and Wang (2011). For some of these models, the point defects in the bulk are confined in meson-like pairs, but the surface excitations are more interesting: The model has deconfined point defects pinned to the boundary of the lattice, and these exhibit exotic (topological) statistics. The surface physics is reminiscent of a fractional quantum hall effect, and these considerations help motivate an effective field theoretic description for the lattice models in their topological limit based on a kind of BF theory. We also discuss another Walker-Wang model that is reminiscent of a 3D bosonic topological insulator, and further clarify its connection to dyonic condensates.