Resource recommendation for fractional statistics

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

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


I'll give you what resources I have on this topic:

General Reviews

  1. Lecture Notes on Anyonic Defects in Condensed Matter

    Lecture notes from a summer school in Florence. A good reference for Majorana zero modes and anyonic defects in condensed matter systems. Large amount of detail--pretty clear.

  2. Braiding with Majorana Fermions

    A good, simple introduction to braiding with anyons and its connection to Majorana fermions. Applications to quantum computing included.

  3. An Anyon Primer

    Excellent introduction to the field with problems, though it can get a little advanced in some places. Applications to the fractional quantum hall effect included.

  4. Quantiki's Introduction to Anyons

    Brief, but possibly a solid starting point. Good links and references as well.

  5. This StackExchange question on non-Abelian anyons in solid state physics might also be useful. See also this StackExchange question for some nice clarifications and links.

Presentations

  1. Fractional Quantum Statistics

    Great presentation on anyons and fractional statistics. Very simple and easily understood. Draws analogies and examples from simple quantum systems. An undergraduate with a background in Griffiths could understand the majority of this presentation.

  2. Fractional Statistics in Two Dimensions: Anyon There?

    Video introducing the concept of anyons to a general audience, from the Perimeter Institute in Waterloo, Ontario. Connections to superconductors are drawn.

Books

  1. Fractional Statistics and Anyon Superconductivity

    Good introduction to the subject by Frank Wilczek, but a bit dated. Has a nice selection of original papers on the topic.

  2. Anyons: Quantum Mechanics of Particles with Fractional Statistics

    By far the best resource on this list. Alberto Lerda's book is the book on anyonic physics, and the best, clearest resource on the subject. Covers a wide range of subject matter, and is understandable at the advanced undergraduate level.

I hope these help. Sorry if there are some duplicates with heather's reply--I tried to list resources that I've found helpful in my own study of fractional statistics.