Fractons and Gapped Boundaries

We investigate gapped boundaries of fracton systems. Fracton phases of matter are 3+1D systems which are fully gapped and translationally invariant but have point-like excitations which are immobile, that is, no local operator moves a single excitation without creating additional particles. Using known exactly solvable models (both “type-I” and “type-II”), we show that particles can be more mobile at surfaces than in the bulk. This change in mobility is well-described by a picture in which excitations condense at the surface; this is similar to gapped boundaries of 2+1D topological order, but our picture applies even to models which are not known to be related to any 2+1D topological order. We then use our condensation picture to investigate what gapped boundaries are possible and discuss a generalization of the Lagrangian subgroup criterion used in standard 2+1D Abelian topological order.