Quasiparticle’s Spin and Fractional Statistics in the Fractional Quantum Hall Effect

  • Dingping Li
Part of the NATO ASI Series book series (NSSB, volume 324)

Abstract

The possibility of fractional statistics on two dimensional surfaces was discovered in Ref. [1–3]. When two fractional-statistics particles (anyons) are interchanged, the wave function changes by a phase exp(), where θ is neither given by θ = 0 (Bose statistics) nor by θ = π (Fermi statistics). Fractional statistics has attracted a lot of attention after it was found that a gas of fractional statistics objects should be superconducting and could provide a mechanism for high-T c superconductivity [4]. Furthermore, the quasiparticles in fractional quantum Hall systems (for a review on the fractional quantum Hall effect (FQHE), see Ref. [5]) are anyons [6, 7] and this picture had been used to construct the hierarchical wave function in the FQHE [7] (for a review, see Refs. [8, 9]). On higher dimensional spaces (D > 2), only Fermions and Bosons exist and the Fermions’ spin is half-integer, the Bosons’ spin is integer. It will be very interesting to know what is the spin of anyons and the spin-statistics relation of anyons. The spin-statistics relation of anyons is a generalized one if the spin s satisfies s = θ/2π. In various models, for example, in non-linear sigma models, Chern-Simons field theories and relativistic quantum field theories on 2D dimensional spaces, anyons indeed satisfy the generalized spin-statistics relation [10, 11]. Naturally, we will ask the question what is the spin-statistics relation of the quasiparticle in the FQHE. Recent discussions of the quasiparticle’s spin (QPS) can be found in Refs. [12–15]. Refs. [12, 13] calculated the QPS by analyzing the hierarchical wave function or by calculating the Berry phase of the quasiparticles moving in a closed path on the sphere. Ref. [14] obtained the QPS by analyzing the Ginzburg-Laudau-Chern-Simons (GLCS) theory of the FQHE on the sphere.

Keywords

Haldane 

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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Dingping Li
    • 1
  1. 1.International School for Advanced studies, SISSATriesteItaly

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