Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundle bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • 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