Anyons and the quantum Hall effect—A pedagogical review
Abstract
The dichotomy between fermions and bosons is at the root of many physical phenomena, from metallic conduction of electricity to superfluidity, and from the periodic table to coherent propagation of light. The dichotomy originates from the symmetry of the quantum mechanical wave function to the interchange of two identical particles. In systems that are confined to two spatial dimensions particles that are neither fermions nor bosons, coined "anyons", may exist. The fractional quantum Hall effect offers an experimental system where this possibility is realized. In this paper we present the concept of anyons, we explain why the observation of the fractional quantum Hall effect almost forces the notion of anyons upon us, and we review several possible ways for a direct observation of the physics of anyons. Furthermore, we devote a large part of the paper to nonabelian anyons, motivating their existence from the point of view of trial wave functions, giving a simple exposition of their relation to conformal field theories, and reviewing several proposals for their direct observation.
 Publication:

Annals of Physics
 Pub Date:
 January 2008
 DOI:
 10.1016/j.aop.2007.10.008
 arXiv:
 arXiv:0711.4697
 Bibcode:
 2008AnPhy.323..204S
 Keywords:

 Condensed Matter  Mesoscale and Nanoscale Physics;
 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 Invited review for the Annals of Physics