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Since non-abelian anyons have become quite fashionable from the point of view of theory. I would like to know, whether there has actually been experimental confirmation of such objects. If you could cite original literature, that would be great!

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  • $\begingroup$ Original literature of what? Theory? Experiment? $\endgroup$ – Qmechanic Dec 18 '13 at 15:46
  • $\begingroup$ Both please! Theoretical description of candidate systems and whether experimental progress has been made. $\endgroup$ – Hamurabi Jan 6 '14 at 11:21
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As far as I know we do not yet have definitive verification of non-abelian statistics which would indicate the existence of non-abelian Anyons. The latest results I know about are the ones mentioned by akhmeteli and An, et. al. "Braiding of Abeliana and Non-Abelian Anyons in the Fractional Quantum Hall Effect." Arxiv:1112.3400. However, I do not believe either are accepted as definitive proof.

You are correct in that there are other candidate systems proposed, such as $p+ip$ superfluids, superconductors, and other systems. Some good references and also a review seem to be given in these review articles. As I understand it, the big push to observe evidence of Majorana fermions. That we do have some pretty good evidence for. Pairs of Majorana fermions are supposed to realize non-abelian statistics, but this has not yet been implemented and observed (to my knowledge).

As a final note, we do have evidence (see here and here) of abelian anyonic statistics, however I am under the impression that there may be some controversy about this.

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Try http://arxiv.org/abs/1301.2639 (Phys. Rev. Lett. 111, 186401 (2013)): "Magnetic field-tuned Aharonov-Bohm oscillations and evidence for non-Abelian anyons at v=5/2" , although I am not sure this is a definite evidence.

"We show that the resistance of the v=5/2 quantum Hall state, confined to an interferometer, oscillates with magnetic field consistent with an Ising-type non-Abelian state."

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  • $\begingroup$ Thanks, but arent there also other candidate systems proposed? Could you also provide links for them, please? $\endgroup$ – Hamurabi Jan 6 '14 at 11:23
  • $\begingroup$ "We stress that the presence of such a period is indicative of a non-Abelian nature of the ν = 5/2 state." Just an indication it seems... $\endgroup$ – Hamurabi Jan 6 '14 at 11:31
  • $\begingroup$ Sorry, I don't think I have anything to add. $\endgroup$ – akhmeteli Jan 7 '14 at 2:40

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