SO(3) NONLINEAR SIGMA-MODEL FOR A DOPED QUANTUM HELIMAGNET

A field theory describing the low-energy, long-wavelength sector of an incommensurate, spiral magnetic phase is derived from a spin-fermion model that is commonly used as a microscopic model for high-temperatur e superconductors. After integrating out the fermions in a path-integr al representation, a gradient expansion of the fermionic determinant i s performed. This leads to an O(3)xO(2)-symmetric quantum nonlinear si gma model, where the doping dependence is explicitly given by generali zed fermionic susceptibilities which enter into the coupling constants of the sigma model and contain the fermionic band-structure that resu lts from the spiral background. A stability condition of the field the ory self-consistently determines the spiral wavevector as a function o f the doping concentration. Furthermore, terms of topological nature l ike the theta-vacuum term in (1+1)-dimensional nonlinear a models are obtained for the plane of the spiral.