condensed matter - Resource recommendation for fractional statistics

A gentle yet comprehensive introduction to the concept of abelian and non-abelian statistics will be much appreciated.

Answer

Abelian

• According to wikipedia, quasiparticles whose statistics range between Fermi-Dirac and Bose-Einstein statistics are called anyons; these particles may only exist in two dimensions. These particles obey fractional statistics, so called because they have fractional spin; see Frank Wilczek's Quantum Mechanics of Fractional-Spin Particles where he also coins the term anyon.


• In the same vein, see Jon Magne Leinaas and Jan Myrheim's paper On the Theory of Identical Particles where they showed quasiparticles can indeed be observed in two dimensions.

Non-abelian

• According to wikipedia, in 1988, Jurg Frohlich showed that non-abelian statistics existed and were valid, in his paper Statistics of Fields, the Yang-Baxter Equation, and the Theory of Knots and Links (note there's a paywall there).


• Again according to wikipedia, Gregory Moore, Nicholas Read, and Xiao-Geng Wen showed non-abelian statistics can be realized in the fractional quantum Hall effect, and wrote two papers, Non-Abelian Statistics in the Fractional Quantum Hall States (Wen) and Nonabelions In the Fractional Quantum Hall Effect (Read and Moore; see section 2.1 in particular).

Other/general

• Fractional Statistics and Quantum Theory (book) by Avinash Khare covers, as the title indicates, anyons and their statistics. The copyright is 1997, so it won't talk much about the applications of anyons to quantum computing; however, it covers pretty much every topic related to abelian/non-abelian statistics as far as I can tell, so if you're willing to pay money (the Google Books sample is decent, but doesn't include every page, obviously) this is probably your best bet. If you do decide this is what you want, the hardcover copy on Amazon is $25, so not too bad compared to a lot of technical books. Mathematical Reviews said
  

  
  
  

  The overall style is clear and pedagogical, with emphasis on symmetry and simplicity.

  
  

  
  


• If you wish to read about the construction of quantum computation theory using anyons, the paper Topological quantum computation will be of use.


• A set of lectures transcribed into a paper on arXiv called Introduction to abelian and non-abelian anyons can be found, and they appear to cover all topics of interest.


• A powerpoint for a talk on Fractional Quantum Statistics also appears to cover everything of interest, though as a powerpoint it may not describe everything in complete detail.

I'll add more papers/books/resources as I find them. Hope these help!