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

- Janusz E. Jacak:
*Topological approach to electron correlations at fractional quantum Hall effect*, Annals of Physics**430**(2021) 168493 [doi:10.1016/j.aop.2021.168493]

$\,$

“Though the Laughlin function very well approximates the true ground state at $\nu = \tfrac{1}{q}$, 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.”

$\,$

]]>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.

]]>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*

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

]]>have added more references:

Steven M. Girvin,

*Introduction to the Fractional Quantum Hall Effect*, Séminaire Poincaré**2**(2004) 53–74, reprinted in*The Quantum Hall Effect*, Progress in Mathematical Physics**45**, Birkhäuser (2005) $[$pdf, doi:10.1007/3-7643-7393-8_4$]$David Tong,

*The Quantum Hall Effect*(2016) $[$course webpage, pdf$]$

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)

- S. Klevtsov, X. Ma, G. Marinescu, P. Wiegmann,
*Quantum Hall effect and Quillen metric*Commun. Math. Phys. 349, 819–855 (2017) doi

Have added references on the theoretical foundations:

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

- R. B. Laughlin,
*Quantized Hall conductivity in two dimensions*, Phys. Rev. B 23, 5632(R) 1981 (doi:10.1103/PhysRevB.23.5632)

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

- Matthew Hastings, Spyridon Michalakis,
*Quantization of Hall Conductance For Interacting Electrons Without Averaging Assumptions*, Commun. Math. Phys., 334:433–471, (2015) (arXiv:0911.4706, doi:10.1007/s00220-014-2167-x)

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:

Yosi Afron,

*Why is the Hall conductance quantized?*, 2017 (pdf, AfronQuantumHallEffect.pdf:file)Spyridon Michalakis,

*Why is the Hall conductance quantized?*, Nature Reviews Physics volume 2, pages 392–393 (2020) (doi:10.1038/s42254-020-0212-6)

I have added pointer to the original article

- Klaus von Klitzing, G. Dorda, and M. Pepper,
*New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance*, Phys. Rev. Lett. 45, 494 (1980) (doi:10.1103/PhysRevLett.45.494)

and to the review

- Klaus von Klitzing,
*The quantized Hall effect*, Rev. Mod. Phys. 58, 519 (1986) (doi:10.1103/RevModPhys.58.519)

Have to interrupt now to do something else…

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

B. I. Halperin,

*Statistics of Quasiparticles and the Hierarchy of Fractional Quantized Hall States*, Phys. Rev. Lett. 52, 1583 (1984) (doi:10.1103/PhysRevLett.52.1583)Erratum Phys. Rev. Lett. 52, 2390 (1984) (doi:10.1103/PhysRevLett.52.2390.4)

Daniel Arovas, J. R. Schrieffer, Frank Wilczek,

*Fractional Statistics and the Quantum Hall Effect*, Phys. Rev. Lett. 53, 722 (1984) (doi:10.1103/PhysRevLett.53.722)

I think I will give this References subsection its own bare entry, for ease of `!include`

-ing it elsewhere, such as at *anyon*

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)

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 (^_^).

Thanks for fixing this! Didn’t notice.

]]>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

- Ludmil Katzarkov, Ernesto Lupercio, Laurent Meersseman, Alberto Verjovsky,
*Noncommutative toric varieties*, arxiv/1308.2774

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

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