Anyons and the quantum Hall effect-A pedagogical review

Journal Article · Tue Jan 15 04:00:00 EST 2008 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2007.10.008· OSTI ID:21077678

Stern, Ady ^[1]

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1. Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100 (Israel)

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.

• OSTI ID: 21077678
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 1 Vol. 323; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANYONS
BOSONS
CONFORMAL INVARIANCE
ELECTRICITY
FERMIONS
HALL EFFECT
QUANTUM FIELD THEORY
QUANTUM MECHANICS
WAVE FUNCTIONS