Fractional Statistics
Martin Greiter, Frank Wilczek

TL;DR
This paper explores the theoretical foundations and experimental evidence of anyons, particles with fractional statistics in two-dimensional quantum systems, highlighting their potential applications in quantum computing.
Contribution
It provides a comprehensive overview of the theory, types, and recent experimental observations of anyons, emphasizing their significance in quantum physics and technology.
Findings
Experimental evidence of anyons in fractional quantum Hall states
Description of non-abelian and mutual statistics of complex anyons
Potential use of anyons in quantum information processing
Abstract
The quantum-mechanical description of assemblies of particles whose motion is confined to two (or one) spatial dimensions offers many possibilities that are distinct from bosons and fermions. We call such particles anyons. The simplest anyons are parameterized by an angular phase parameter . correspond to bosons and fermions respectively; at intermediate values we say that we have fractional statistics. In two dimensions, describes the phase acquired by the wave function as two anyons wind around one another counterclockwise. It generates a shift in the allowed values for the relative angular momentum. Composites of localized electric charge and magnetic flux associated with an abelian U(1) gauge group realize this behavior. More complex charge-flux constructions can involve non-abelian and product groups acting on a spectrum of allowed charges and…
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Taxonomy
TopicsQuantum and electron transport phenomena · Surface and Thin Film Phenomena · Physics of Superconductivity and Magnetism
