added pointer to today’s

- Andrey Morozov,
*On measuring the topological charge of anyons*[arXiv:2403.07847]

added pointer to this article:

- Roberto Iengo, Kurt Lechner,
*Anyon quantum mechanics and Chern-Simons theory*, Physics Reports**213**4 (1992) 179-269 [doi:10.1016/0370-1573(92)90039-3]

added pointer to the recent:

- Martin Greiter, Frank Wilczek,
*Fractional Statistics*[arXiv:2210.02530]

added pointer to:

- Parsa Bonderson, Kirill Shtengel, Joost Slingerland,
*Interferometry of non-Abelian Anyons*, Annals Phys.**323**(2008) 2709-2755 [doi:10.1016/j.aop.2008.01.012, arXiv:0707.4206]

added (here) brief pointer to and a figure from

- Michele Correggi, Romain Duboscq, Douglas Lundholm, Nicolas Rougerie,
*Vortex patterns in the almost-bosonic anyon gas*, Europhys. Lett.**126**(2019), 20005 [arXiv:1901.10739, doi:10.1209/0295-5075/126/20005]

I have added (here) a further reference/quote on anyons appearing as defects

]]>above my definition of “adiabatic defect braiding” (here), I have added more and more authorative reference which agree with this (or would, if they thought of stating definitions).

]]>of course that’s essentially already the statement of

- Yong-Shi Wu,
*Multiparticle Quantum Mechanics Obeying Fractional Statistics*, Phys. Rev. Lett.**53**(1984) 111 $[$doi:10.1103/PhysRevLett.53.111, pdf$]$

albeit not quite as explicitly

]]>Finally found authors admitting this here:

If $\theta \in\!\!\!\!\!/ \frac{1}{2}\mathbb{Z}$ the Hilbert space of anyon wave functions must be chosen to be a space of multi-valued functions with half-monodromies given by the phase factors $exp(2 \pi \mathrm{i} \theta)$. Such wave functions can be viewed as single-valued functions on the universal cover $\widetilde M_n$ of $M_n$ $[$the configuration space of points$]$.

Namely, p. 20 in:

- Jürg Fröhlich, Fabrizio Gabbiani, Pieralberto Marchetti,
*Braid statistics in three-dimensional local quantum field theory*, in: H.C. Lee (ed.)*Physics, Geometry and Topology*NATO ASI Series,**238**Springer (1990) $[$doi:10.1007/978-1-4615-3802-8_2, pdf$]$

have further worked on the Idea-section (here), now highlighting that one may recognize in the literature two different mathematical conceptualizations of anyon statistics, which the entry now refers to as *anyonic quanta* and as *anyonic defects*, respectively

started adding a section *As a “fictitious” Aharonov-Bohm effect* (here) on the model due to

- Yi-Hong Chen, Frank Wilczek, Edward Witten, Bertrand Halperin,
*On Anyon Superconductivity*, International Journal of Modern Physics B**03**07 (1989) 1001-1067 (reprinted in Wilczek 1990) $[$doi:10.1142/S0217979289000725, CWWH-AnyonSuperfluidity.pdf:file$]$

I have further worked on the Idea section (now called “Anyon braiding”, here*) further trying to bring out the issue as in #8 by adding/point to more of the original references.

]]>added this pointer:

- Yi-Hong Chen, Frank Wilczek, Edward Witten, Bertrand Halperin,
*On Anyon Superconductivity*, International Journal of Modern Physics B**03**07 (1989) 1001-1067 $[$doi:10.1142/S0217979289000725, pdf $]$

pointer to this book had been missing:

- Frank Wilczek,
*Fractional Statistics and Anyon Superconductivity*, World Scientific (1990) $[$doi:10.1142/0961$]$

have added pointer (here) to vortex anyons with bound Majorana zero modes, and included the graphics from Fig. 1 here.

]]>I have re-worked and substantially expanded the Idea-section (here).

This could (and should) be expanded much further, of course.

For the moment the point I tried to bring out is that the literature is a little undecided about two somewhat different conceptualization of what counts as an *anyon*: one being associated with the term “quasiparticle”, the other really being *solitonic defects*.

Even on just this point one could and should expand further. But so much for now.

]]>added (here) a commented list of references on “defect anyons”.

Will put this list into a separate page now and re-`!include`

it here.

added references (here) on “anyonic braiding in momentum space”

(had collected these in April already, for this MO reply, but back then the nLab was down)

will give this list its own stand-alone entry to be `!include`

-ed here, since the same list should also go at *semi-metal*

added pointer to:

- Liang Wang, Zhenghan Wang,
*In and around Abelian anyon models*, J. Phys. A: Math. Theor.**53**505203 (2020) (doi:10.1088/1751-8121/abc6c0)

am now adding references on the other kind of anyon excitations, not in quantum Hall liquids but in topological superconductors. (Will move this into a separate page, to be `!include`

-ed here.)

So far I have:

via Majorana zero modes:

Original proposal:

- N. Read, Dmitry Green,
*Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect*, Phys. Rev. B61:10267, 2000 (arXiv:cond-mat/9906453)

Review:

Sankar Das Sarma, Michael Freedman, Chetan Nayak,

*Majorana Zero Modes and Topological Quantum Computation*, npj Quantum Information 1, 15001 (2015) (nature:npjqi20151)Nur R. Ayukaryana, Mohammad H. Fauzi, Eddwi H. Hasdeo,

*The quest and hope of Majorana zero modes in topological superconductor for fault-tolerant quantum computing: an introductory overview*(arXiv:2009.07764)

via Majorana zero modes restricted to edges of topological insulators:

- Biao Lian, Xiao-Qi Sun, Abolhassan Vaezi, Xiao-Liang Qi, and Shou-Cheng Zhang,
*Topological quantum computation based on chiral Majorana fermions*, PNAS October 23, 2018 115 (43) 10938-10942; first published October 8, 2018 (doi:10.1073/pnas.1810003115)

Have been expanding the list of references a little: more of the original articles, and more reviews.

On the actual experimental confirmation of anyons, it seems the first robust result is from last year(!):

- James Nakamura, Shuang Liang, Geoffrey C. Gardner, Michael J. Manfra,
*Direct observation of anyonic braiding statistics*, Nat. Phys. 16, 931–936 (2020). (arXiv:2006.14115, doi:10.1038/s41567-020-1019-1)

I am adding missing cross-links *anyon – quantum Hall effect – quantum computation*

In the process, I have added this reference:

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

stub for *braid group statistics* (again, for the moment mainly in order to record a reference)