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Ground State Degeneracy of Topological Phases on Open Surfaces · Around

2014

Ground State Degeneracy of Topological Phases on Open Surfaces

Hung, Ling-Yan, Wan, Yidun

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We relate the ground state degeneracy (GSD) of a non-Abelian topological phase on a surface with boundaries to the anyon condensates that break the topological phase to a trivial phase.

Specifically, we propose that gapped boundary conditions of the surface are in one-to-one correspondence to the sets of condensates, each being able to completely break the phase, and we substantiate this by examples.
The GSD 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-Wu-Tao (LWT) charge-pumping argument for Abelian fractional quantum Hall states (FQHS) to encompass non-Abelian topological phases, in the sense that an anyon loop of a confined anyon winding a non-trivial cycle can pump a condensate from one boundary to another.

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