Flux States,Anyons and High Tc Superconductivity

In this paper, we studied the statistical behavior of anyons with isospin degrees of freedom, in which the fluctuation of isospjn 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 an tiferromagnetic (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.