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nLab > Latest Changes: anyonic topological order via braided fusion categories -- references

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJun 7th 2022
    • (edited Jun 7th 2022)

    This is a bare list of references, to be !include-ed into the References-lists of relevant entries (such as at anyon, topological order, fusion category, unitary fusion category, modular tensor category).

    There is a question which I am after here:

    • This seems to be CMT folklore, as all authors state it without argument or reference.

      Who is really the originator of the claim that anyonic topological order is characterized by certain unitary braided fusions categories/MTCs?

    Is it Kitaev 06 (which argues via a concrete model, in Section 8 and appendix E)?

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeSep 10th 2022
    • (edited Sep 10th 2022)

    have taken the liberty of adding these pointers:

    Emphasis that the expected description of anyons by braided fusion categories had remained folklore, together with a list of minimal assumptions that would need to be shown:

    An argument that the statement at least for SU(2)-anyons does follow from an enhancement of the K-theory classification of topological phases of matter to interacting topological order:

    diff, v4, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeOct 19th 2022

    added pointer to

    • Liang Kong, Topological Wick Rotation and Holographic Dualities, talk at CQTS (Oct 2022) [pdf]

    diff, v8, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeNov 9th 2022

    added pointer to today’s

    diff, v9, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeDec 5th 2022

    added pointer to today’s:

    • Willie Aboumrad, Quantum computing with anyons: an F-matrix and braid calculator [[arXiv:2212.00831]]

    diff, v11, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeMar 10th 2023

    added pointer to:

    Took that as occasion to subdivide this !include-subsection further into two sub-subsection: “Claim and status” and “Further discussion”.

    diff, v13, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeMar 29th 2023

    added pointer to:

    diff, v14, current

1 to 7 of 7

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