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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMay 25th 2022

    a bare list of references, to be !include-ed into the References-section of relevant entries (such as at braid group representation and at semi-metal).

    Had originally compiled this list already last April (for this MO reply) but back then the nLab couldnt be edited

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMay 28th 2022

    added more items and more quotes

    diff, v4, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJun 8th 2022
    • (edited Jun 8th 2022)

    I’d also like to compile a list of references which admit or at least indicate that the usual hope of having anyonic topological order on a toroidal (or even higher genus) position space is dubious.

    I had come across several such references in the past, but didn’t record them in this respect. So now I need to re-compile a list. For the moment I have

    which is quite explicit.

    I vividly remember a reference on the alleged classification of topological order by FQFT/cobordism which tried to argue that crystal impurities could mimic higher genus position space geometries. But it seems I have lost it and now it’s the proverbial needle in the haystack.

    diff, v7, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeAug 27th 2022
    • (edited Aug 27th 2022)

    added pointer to:

    with this quote:

    Here, we consider an exotic type of topological phases beyond the above paradigms that, instead, depend on topological charge conversion processes when band nodes are braided with respect to each other in momentum space or recombined over the Brillouin zone. The braiding of band nodes is in some sense the reciprocal space analog of the non-Abelian braiding of particles in real space.


    we experimentally observe non-Abelian topological semimetals and their evolutions using acoustic Bloch bands in kagome acoustic metamaterials. By tuning the geometry of the metamaterials, we experimentally confirm the creation, annihilation, moving, merging and splitting of the topological band nodes in multiple bandgaps and the associated non-Abelian topological phase transitions

    diff, v8, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeAug 27th 2022

    also pointer to:

    • Jian Kang, Oskar Vafek, Non-Abelian Dirac node braiding and near-degeneracy of correlated phases at odd integer filling in magic angle twisted bilayer graphene, Phys. Rev. B 102 (2020) 035161 [arXiv:2002.10360, doi:10.1103/PhysRevB.102.035161]

    which stands out as discussion the phenomen for (twisted bilayer-) graphene

    diff, v9, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeAug 30th 2022

    added pointer to today’s

    diff, v10, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeMar 7th 2023

    added a warning:

    Beware that various authors consider braids/knots formed by nodal lines in 3d semimetals, i.e. knotted nodal lines in 3 spatial dimensions, as opposed to worldlines of nodal points in 2+1 spacetime dimensions needed for anyon-braiding as considered above.

    and then, to start with, pointer to this argument that these nodal lines in 3d space, nevertheless, may be controlled by Chern-Simons theory:

    diff, v20, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeMay 5th 2023

    added pointer to this recent article:

    • Huahui Qiu et al., Minimal non-abelian nodal braiding in ideal metamaterials, Nature Communications 14 1261 (2023) [[doi:10.1038/s41467-023-36952-9]]

    diff, v22, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeMay 28th 2024
    • (edited May 28th 2024)

    added pointer to:

    • Seung Hun Lee, Yuting Qian, Bohm-Jung Yang, Euler band topology in spin-orbit coupled magnetic systems [arXiv:2404.16383]

    with this quote:

    “Based on first-principles calculations, we report that such nodal point braiding in 2D electronic bands can be realized in a MSWI candidate, the bilayer ZrTe 5ZrTe_5 with in-plane ferromagnetism under pressure. […] one can expect that the braiding of nodes can be achieved in 2D bilayer ZrTe 5ZrTe_5 under the influence of an external in-plane Zeeman field.”

    diff, v26, current