Braiding and Gapped Boundaries in Fracton Topological Phases

Understand

We study gapped boundaries of Abelian type-I fracton systems in three spatial dimensions.

• Using the X-cube model as our motivating example, we give a conjecture, with partial proof, of the conditions for a boundary to be gapped.
• In order to state our conjecture, we use a precise definition of fracton braiding and show that bulk braiding of fractons has several features that make it \textit{insufficient} to classify gapped boundaries.
• Most notable among these is that bulk braiding is sensitive to geometry and is "nonreciprocal," that is, braiding an excitation $a$ around $b$ need not yield the same phase as braiding $b$ around $a$.