Ground-state degeneracy of topological phases on open surfaces

Physical Review Letters
Ling-Yan Hung, Yidun Wan

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.

References

Mar 15, 1985·Physical Review. B, Condensed Matter·Q NiuY S Wu
Oct 1, 1989·Physical Review. B, Condensed Matter·X G Wen
Jun 15, 1990·Physical Review. B, Condensed Matter·X G Wen
Oct 26, 2002·Physical Review Letters·F A BaisJ K Slingerland
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Nov 8, 2014·Science·Maissam BarkeshliSteven Kivelson
Mar 13, 2015·Physical Review Letters·Tian LanXiao-Gang Wen

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Citations

Jan 1, 2017·Physical Review. B·Sriram GaneshanVictor M Galitski
Mar 13, 2015·Physical Review Letters·Tian LanXiao-Gang Wen
Sep 7, 2019·Physical Review Letters·Ce Shen, Ling-Yan Hung
Apr 24, 2021·Physical Review Letters·Bowen Shi, Isaac H Kim

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