Anyons and the quantum Hall effect - a pedagogical review
arXiv:0711.4697 · doi:10.1016/j.aop.2007.10.008
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.
Invited review for the Annals of Physics
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Cited by in corpus (9)
- Non-Abelian Anyons and Topological Quantum Computation
- Stable Topological Superfluid Phase of Ultracold Polar Fermionic Molecules
- Implementation of Clifford gates in the Ising-anyon topological quantum computer
- Near zero modes in condensate phases of the Dirac theory on the honeycomb lattice
- Observable Bulk Signatures of Non-Abelian Quantum Hall States
- Coulomb blockade as a probe for non-Abelian statistics in Read-Rezayi states
- Experimental signatures of non-Abelian statistics in clustered quantum Hall states
- Electron interferometry in quantum Hall regime: Aharonov-Bohm effect of interacting electrons
- Low-field quantum Hall transport in an electron Fabry-Perot interferometer: Determination of constriction filling vs front-gate voltage