期刊
PHYSICAL REVIEW LETTERS
卷 114, 期 7, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.114.076401
关键词
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资金
- Croucher Fellowship
- John Templeton Foundation
- Government of Canada through Industry Canada
- Province of Ontario through the Ministry of Economic Development Innovation
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.
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