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nLab > Latest Changes: Laughlin wavefunction

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJun 7th 2022

    starting something – remains a stub for the moment, to be continued

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJun 7th 2022

    What I am really after, for the moment, is whether the idea that is visible in equation (3) of

    has been picked up and developed elsewhere: Essentially two types of anyons, the first type with a fixed pairwise braiding phase, and then another braiding phase when the first type braids around the second.

    diff, v3, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeFeb 20th 2023

    added pointer to:

    diff, v9, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJan 8th 2025

    have started adding some actual content:

    1. a couple of paragraphs on the general idea,

    2. the basic Laughlin wavefunction

    3. the basic Moore & Read wavefunction

    4. the “supersymmetry” relation between them

    (Leaving much, much room to further expand, but it’s a start.)

    diff, v15, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJan 9th 2025
    • (edited Jan 9th 2025)

    I am deleting this reference:

    because now that I looked at it more closely, I can’t make sense of it.

    (Culminating around its equation (25), this article argues that the FQH Laughlin wavefunction follows from the integer one by demanding that it picks up phases e iπqe^{\mathrm{i} \pi q}. But qq is an odd integer, so that e iπq=e iπe^{\mathrm{i} \pi q} = e^{\mathrm{i} \pi} and the argument is void. Generally, the conceptual problem seems to be that the author is (trying to) think of the electrons in the Laughlin state as abelian anyons, while instead it’s the “quasi-holes/particles” in the electron fluid which are anyonic.)

    diff, v18, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJan 11th 2025

    added pointer to:

    (also at fractional quantum Hall effect)

    diff, v21, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeJan 12th 2025

    finally also some paragraphs on the Laughlin state with “quasi-holes” (now here)

    diff, v24, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTime5 days ago

    added a further section “GMP-Excitations of Laughlin states” (here), following the super-space formulation of Gromov, Martinec & Ryu 2020

    diff, v29, current

1 to 8 of 8

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