Fractional statistics: alpha to beta

Abstract

We review the problem of fractional statistics as it applies to two current areas of interest in condensed-matter physics: the fractional quantum Hall effect (FQHE), and high-temperature superconductors (HTSC). In the case of the former, we emphasize Haldane's recent definition (1991) of a fractional exclusion principle, and show a relation between this idea and the standard definition of fractional statistics in terms of a complex exchange phase. We show that a fractional exclusion principle is both appropriate and useful for the quasiparticles in the FQHE. In the case of the HTSC (where Haldane's novel definition has not been pursued), we review the experimental status of the 'anyon superconductivity' model for the HTSC. Here we find much less support for the hypothesis that the excitations are anyons. We also argue that the past neglect of Haldane's fractional exclusion principle makes tile resulting theory inconsistent.