Spin and charge fluctuations in a one-dimensional lattice with long-range interactions

We study the competition between spin and charge fluctuations of the extended Hubbard model with on-site and dipole-dipole interactions in a one-dimensional lattice. Using the extended two-particle self consistent (ETPSC) method, we find the corresponding expressions for spin and charge response functions. In this approach, the irreducible spin and charge vertices are a function of inter-particle distance (r) and wave-number (q). This theory allows us to determine the crossover temperatures and the dominant instability as a function of U and V. The phase diagrams are obtained for several effective particle densities: n=0.5, n=1 and n=4/3. Each phase diagram (U-V-T space) incorporates four possible modulations of charge carriers and spins like charge/spin density wave, phase-separation and paramagnetic orders. We find that the portion of possible phases depending on the on-site interaction U, nearest-neighbor interaction V and filling factor n can change.