Chiral spin state and anyons in extended t−J model

The extended t − J model has been studied within a mean field approximation by use of the slave boson scheme. It is found that there exists some range of parameters where the chiral spin state is stabilized. The Chern-Simons Lagrangian for the gauge field, which represents the fluctuation of the phases of the order parameters and the local constraint, is obtained by integrating out spin fermion fields as in the undoped case studied by Wen, Wilczek and Zee. The coefficient of this term turns out to depend on doping. Due to the coupling to this Chern-Simons gauge field, hole bosons are transmuted into anyons.