title: Ground-state degeneracy of topological phases on open surfaces.
abstract: We relate the ground state degeneracy of a non-Abelian topological phase on a surface with boundaries to the anyon condensates that break the topological phase into a trivial phase. Specifically, we propose that gapped boundary conditions of the surface are in one-to-one correspondence with the sets of condensates, each being able to completely break the phase, and we substantiate this by examples. The ground state degeneracy resulting from a particular boundary condition coincides with the number of confined topological sectors due to the corresponding condensation. These lead to a generalization of the Laughlin-Tao-Wu charge-pumping argument for Abelian fractional quantum Hall states to encompass non-Abelian topological phases, in the sense that an anyon loop of a confined anyon winding a nontrivial cycle can pump a condensed anyon from one boundary to another. Such generalized pumping may find applications in quantum control of anyons, eventually realizing topological quantum computation.
authors.affiliation: Department of Physics and Center for Field Theory and Particle Physics, Fudan University, Shanghai 200433, China.|Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.
authors.forename: Ling-Yan
authors.initials: LY
authors.lastname: Hung
authors.affiliation: Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada.
authors.forename: Yidun
authors.initials: Y
authors.lastname: Wan