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Physics Letters A

Non-identical anyons and new statistics for spinons and holons

Tal Mor

Published Dec 1, 1993• 1 citation
Publisher
DOI
10.1016/0375-9601(93)90341-v

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In this paper, we studied the statistical behavior of anyons with isospin degrees of freedom, in which the fluctuation of isospin degrees of freedom satisfies the O(3) nonlinear σ model. Under the mean field treatment, this model is in somewhat equivalent to the doped or frustrated Heisenberg antiferromagnetic (AFM) model. We also studied the relation between the statistical field A μ , and Skyrmion current B μ . Finally, we set up the relation between flux states and spinon statistics, and the conditions of Bose condensation of holons. In particular, for π -flux state of A μ , the spinons are bosons, the holons satisfy 2/3 fractional statistics.
A topological argument similar to that of Leinaas and Myrheim implies that a non-trivial statistical phase factor can also arise from exchanging twice a pair of distinguishable particles in two dimensions. Some general properties of this phase factor are deduced. Wilczek's model for anyons and the Laughlin theory for the quasiparticles in the fractional quantum Hall ground states are examined in light of these properties, and the former is generalized for systems containing many species of anyons. The statistical properties of holons and spinons relative to each other are briefly discussed as an example.