# What is the precise definition or list of prerequisites for an anyonic system?

I have been reading some reviews and looked into books on anyons and topological quantum computation and I found it a little difficult to make out a short list of parameters and a clear and short list of mathematical structures needed to define an anyonic system. I would like to ask for help here. In Nayak et al.'s review I found the following list and would like to know, whether it is complete:

1. particle species
2. fusion rules
3. F-matrix for recoupling of the anyonic charges
4. R-matrix for the braiding
5. topological spins
6. S-matrix

For the maths structure, one needs a ribbon fusion category. Is this enough? And that about the spin is associated to $SO(2)$? Do I need to add a statement about that also into the list?

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I guess the first question is: what is an anyonic system? I went to a talk by Xiao-Gang Wen some time ago about systems which are exactly anyonic at some critical point, but not-quite-anyonic near this point. If you are talking about these systems, off the critical point, then you will need more parameters to describe them. And if these systems exist in theory, they are likely to exist in real materials. Do they count as anyonic systems? –  Peter Shor Jan 24 at 15:15
Is nobody going to post an answer? Let me say that Chetan Nayak and his coauthors know what they are talking about. If you're looking for a "credible source" (as you claim in your bounty), you are probably not going to find a better one. –  Peter Shor Jan 27 at 1:19
I am sure they know what they are talking about. I never doubted that. However, I personally find it difficult to find a source where clearly it stands (and not hidden in between the lines) like this: "For an anyon model we need precisely this and that. Full stop. Variations are the e.g. ..." –  Hamurabi Jan 28 at 22:48
@Hamurabi you should urgently avoid the term "list" and edit it out of your question. Any sorts of lists are not allowed here, and the mods will immediately close your question as soon as they see it. Not my idea however... –  Dilaton Mar 13 at 11:12