Effective action and collective modes in quasi-one-dimensional spin-density-wave systems

We derive the effective action describing the long-wavelength low-energy co llective modes of quasi-one-dimensional spin-density-wave (SDW) systems, st arting from the Hubbard model within a weak coupling approximation. The eff ective action for the spin-wave mode corresponds to an anisotropic nonlinea r sigma model together with a Berry phase term. We compute the spin stiffne ss and the spin-wave velocity. We also obtain the effective action for the sliding mode (phason) taking into account the density fluctuations from the outset and in the presence of a weak external electromagnetic field. This leads to coupled equations for the phase of the SDW condensate and the char ge-density fluctuations. We also calculate the conductivity and the density -density correlation function.