Fluctuation Effect in the π-Flux State for Undoped High-Temperature Superconductors

The effect of fluctuations about the pi-flux mean field state for the undoped high-temperature superconductors is investigated. It is shown that fluctuations of the mean fields lead to a self-energy correction that doubles the band width of the fermion dispersion in the lowest order. The dynamical mass generation is associated with the self-enemy effect due to the interaction mediated by the Lagrange multiplier field, which is introduced to impose the constraint on the fermions. A self-consistent picture about the mass generation and the propagation of the Lagrange multiplier field without damping is proposed. The antiferromagnetic long-range ordering is described without introducing an additional repulsive interaction. The theory suggests a natural framework to study spin disordered systems in which fermionic excitations are low-lying excitations.