# Start a new discussion

## Not signed in

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

## Site Tag Cloud

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

• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeMay 14th 2012

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

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeFeb 12th 2021

I am adding missing cross-links anyonquantum Hall effectquantum 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)
• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeFeb 14th 2021

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(!):

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeFeb 17th 2021

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:

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:

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)
• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeDec 25th 2021

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeMay 25th 2022

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

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeMay 28th 2022
• (edited May 28th 2022)

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

Will put this list into a separate page now and re-!include it here.

• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeMay 29th 2022
• (edited May 29th 2022)

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.

• CommentRowNumber9.
• CommentAuthorUrs
• CommentTimeMay 30th 2022

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

• CommentRowNumber10.
• CommentAuthorUrs
• CommentTimeMay 31st 2022
• (edited May 31st 2022)

pointer to this book had been missing:

• Frank Wilczek, Fractional Statistics and Anyon Superconductivity, World Scientific (1990) $[$doi:10.1142/0961$]$
• CommentRowNumber11.
• CommentAuthorUrs
• CommentTimeJun 1st 2022

• CommentRowNumber12.
• CommentAuthorUrs
• CommentTimeJun 1st 2022

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.

• CommentRowNumber13.
• CommentAuthorUrs
• CommentTimeJun 4th 2022

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

• CommentRowNumber14.
• CommentAuthorUrs
• CommentTimeJun 4th 2022
• (edited Jun 4th 2022)

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

• CommentRowNumber15.
• CommentAuthorUrs
• CommentTimeJun 4th 2022
• (edited Jun 4th 2022)

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:

• CommentRowNumber16.
• CommentAuthorUrs
• CommentTimeJun 4th 2022

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

• CommentRowNumber17.
• CommentAuthorUrs
• CommentTimeJun 11th 2022

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).

• CommentRowNumber18.
• CommentAuthorUrs
• CommentTimeJun 14th 2022

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

• CommentRowNumber19.
• CommentAuthorUrs
• CommentTimeSep 2nd 2022

added (here) brief pointer to and a figure from

• Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
• To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

• (Help)