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

We derive the effective action describing the long-wavelength low-energy collective modes of quasi-one-dimensional spin-density-wave (SDW) systems, starting from the Hubbard model within weak coupling approximation. The effective action for the spin-wave mode corresponds to an anisotropic non-linear sigma model together with a Berry phase term. We compute the spin stiffness 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 presence of a weak external electromagnetic field. This leads to coupled equations for the phase of the SDW condensate and the charge density fluctuations. We also calculate the conductivity and the density-density correlation function.