PossibleT- andP-breaking vacua of O(3) nonlinearσmodel and spin-charge separation

We discuss possible quantum disordered states of the O(3) nonlinear {σ} model in which time-reversal invariance (T) and parity (P) are spontaneously broken. We show that there is spin-charge separation in these T- and P-broken disordered states. In one of the disordered states the quasiparticles are half-fermions, or semions, as in the Kalmeyer-Laughlin approach to the resonating-valence-bond state. We also write down the effective Lagrangian for the quasiparticles in these disordered phases.