Anyons and the quantum Hall effect - a pedagogical review

TL;DR

This pedagogical review explains the concept of anyons, their role in the fractional quantum Hall effect, and discusses methods for their direct observation, including non-abelian anyons and their theoretical foundations.

Contribution

It provides a comprehensive, accessible overview of anyons, linking their theoretical basis to experimental detection strategies, especially in the context of the fractional quantum Hall effect.

Findings

Explanation of anyons and their significance in 2D systems

Review of experimental approaches for observing anyons

Discussion of non-abelian anyons and their theoretical connections

Abstract

The dichotomy between fermions and bosons is at the root of many physical phenomena, from metallic conduction of electricity to super-fluidity, 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 non-abelian 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.