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arXiv · 1408.0014

Ground State Degeneracy of Topological Phases on Open Surfaces

Ling-Yan Hung·Yidun Wan
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Abstract

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. Such generalized pumping may find applications in quantum control of anyons, eventually realizing topological quantum computation.

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Ling-Yan Hung, Yidun Wan. 2015-02-22. Ground State Degeneracy of Topological Phases on Open Surfaces. https://doi.org/10.1103/physrevlett.114.076401

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