Ground-state degeneracy for Abelian anyons in the presence of gapped boundaries

Abstract

Gapped phases with long-range entanglement may admit gapped boundaries. If the boundary is gapped, the ground-state degeneracy is well defined and can be computed using methods of topological quantum field theory. We derive a general formula for the ground-state degeneracy for Abelian fractional quantum Hall phases, including the cases when connected components of the boundary are subdivided into an arbitrary number of segments, with a different boundary condition on each segment, and in the presence of an arbitrary number of boundary domain walls.