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nLab > Latest Changes: quantum Hall effect

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  1.  
    • CommentRowNumber1.
    • CommentAuthorzskoda
    • CommentTimeSep 20th 2013

    Unfortunately, there are two entries on the same topic, both created by Urs: quantum Hall effect (redirecting also fractional quantum Hall effect what should eventually split off) with some substance, and the microstub quantum hall effect. I would like to create quantum spin Hall effect and I think I should rename/reclaim the stub quantum hall effect for this. Do others agree ? Urs ?

    As the action is now delayed I record here the reference which I wanted to put there

    • B. Andrei Bernevig, Taylor L. Hughes, Shou-Cheng Zhang, Quantum spin Hall rffect and topological phase transition in HgTe quantum wells, Science 15 December 2006: 314, n. 5806, pp. 1757-1761 doi

    Somewhat surprisingly, the authors and roughly this work of them are mentioned (though not in the list of references) in a paper in algebraic geometry

    which considers the mirror symmetry and topological states of matters (topological insulators in particular) as main applications.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeSep 20th 2013

    Thanks for fixing this! Didn’t notice.

    • CommentRowNumber3.
    • CommentAuthorTobyBartels
    • CommentTimeSep 21st 2013

    The theoretically proper thing to do is to move (change page name) quantum hall effect to quantum hall effect > history (while replacing its content with < [[quantum hall effect]] and of course putting [[!redirects quantum hall effect]] at quantum Hall effect).

    After saying all that, I decided to just do it. So I did it.

    However, since there is no actual additional content, nor even any edit history of such, it actually doesn't matter if you do as you propose instead. In particular, if you'd like to have Urs's ministub in the history of your page, then go to quantum hall effect > history (or even revision 1) and rename and edit it. I won't be upset (^_^).

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeFeb 12th 2021

    I have added missing publication data for this item:

    • Chetan Nayak, Steven H. Simon, Ady Stern, Michael Freedman, Sankar Das Sarma, Non-Abelian Anyons and Topological Quantum Computation, Rev. Mod. Phys. 80, 1083, 2008([arXiv:0707.1888] (http://arxiv.org/abs/0707.1889), doi:10.1103/RevModPhys.80.1083)

    And added this more recent pointer:

    • Ville Lahtinen, Jiannis K. Pachos, A Short Introduction to Topological Quantum Computation, SciPost Phys. 3, 021 (2017) (arXiv:1705.04103)

    diff, v6, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeFeb 15th 2021

    I have added the original references predicting abelian anyons in the FQHE:

    I think I will give this References subsection its own bare entry, for ease of !include-ing it elsewhere, such as at anyon

    diff, v10, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeFeb 17th 2021

    I have added pointer to the original article

    and to the review

    Have to interrupt now to do something else…

    diff, v12, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeFeb 18th 2021

    Have added references on the theoretical foundations:

    While an intuitive understanding for the quantization of the Hall conductance has been given in

    a theoretical derivation of the effect was obtained only much later in

    with closely related results in

    • Alessandro Giuliani, Vieri Mastropietro, Marcello Porta, Universality of the Hall conductivity in interacting electron systems, Communications in Mathematical Physics volume 349, pages 1107–1161(2017) (arXiv:1511.04047, doi:10.1007/s00220-016-2714-8)

    Review of this theory behind the quantum Hall effect:

    diff, v13, current

    • CommentRowNumber8.
    • CommentAuthorzskoda
    • CommentTimeAug 19th 2021
    • S. Klevtsov, X. Ma, G. Marinescu, P. Wiegmann, Quantum Hall effect and Quillen metric Commun. Math. Phys. 349, 819–855 (2017) doi

    diff, v15, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeNov 17th 2021

    added pointer to today’s

    • William Wolf, James Read, Nicholas Teh, Edge modes and dressing fields for the Newton-Cartan quantum Hall effect (arXiv:2111.08052)

    diff, v16, current

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeJun 8th 2022

    have added more references:

    diff, v22, current

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeAug 17th 2024

    started adding references (here) on microscopic models for the FQHE

    diff, v27, current

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeAug 17th 2024

    started a section (here) with references relating the QHE to noncommutative geometry

    will make this now an !include-file, so that it can be easily referenced also at noncommutative geometry and maybe also at matrix model

    diff, v28, current

    • CommentRowNumber13.
    • CommentAuthorUrs
    • CommentTimeAug 18th 2024
    • (edited Aug 18th 2024)

    have been adding various further references on the fractional quantum Hall effect.

    Last night I had a reference that was nicely explicit about the fact that — despite the existing “microscopic” models (here) — a first-principles derivation/explanation of the effect actually remains elusive. But this morning I seem to have lost that reference and forgotten its title.

    diff, v31, current

    • CommentRowNumber14.
    • CommentAuthorUrs
    • CommentTimeAug 18th 2024
    • (edited Aug 18th 2024)

    Not the reference which I saw yesterday, but makes the desired point quite explicit:

    \,

    “Though the Laughlin function very well approximates the true ground state at ν=1q\nu = \tfrac{1}{q}, the physical mechanism of related correlations and of the whole hierarchy of the FQHE remained, however, still obscure.”

    “the Halperin multicomponent theory and of the CF model advanced the understanding of correlations in FQHE, however, on a phenomenological level only. CFs were assumed to be hypothetical quasi-particles consisting of electrons and flux quanta of an auxiliary fictitious magnetic field pinned to them. The origin of this field and the manner of attachment of its flux quanta to electrons have been neither explained nor discussed.”

    \,

    diff, v34, current

    • CommentRowNumber15.
    • CommentAuthorUrs
    • CommentTimeSep 23rd 2024
    • (edited Sep 23rd 2024)

    I have re-written the previous paragraph in the Idea section (though it’s still not meant to be more than a placeholder)

    and then I reproduced (here) excerpts from the really nice text of Störmer 1999, including a couple of graphics, regarding the “composite particle” interpretation of the FQHE.

    diff, v35, current

1 to 15 of 15

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