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stub for braid group statistics (again, for the moment mainly in order to record a reference)
I am adding missing cross-links anyon – quantum Hall effect – quantum computation
In the process, I have added this reference:
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(!):
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:
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:
added pointer to:
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
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.
have added pointer (here) to vortex anyons with bound Majorana zero modes, and included the graphics from Fig. 1 here.
pointer to this book had been missing:
added this pointer:
started adding a section As a “fictitious” Aharonov-Bohm effect (here) on the model due to
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
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:
of course that’s essentially already the statement of
albeit not quite as explicitly
added (here) brief pointer to and a figure from
added pointer to:
added pointer to the recent:
added pointer to this article:
added pointer to today’s
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