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We investigate charge ordering in the presence of electron-phonon coupling for quarter-filled ladder systems by using Exact Diagonalization. As an example we consider NaV2O5 using model parameters obtained from first-principles band-structure calculations. The relevant Holstein coupling to the lattice considerably reduces the critical value of the nearest-neighbor Coulomb repulsion at which formation of the zig-zag charge-ordered state occurs, which is then accompanied by a static lattice distortion. Energy and length of a kink-like excitation on the background of the distorted lattice are calculated. Spin and charge spectra on ladders with and without static distortion are obtained, and the charge gap and the effective spin-spin exchange parameter J are extracted. J agrees well with experimental results. Analysis of the dynamical Holstein model, restricted to a small number of phonons, shows that low frequency lattice vibrations increase the charge order, accompanied by dynamically produced zig-zag lattice distortions.Comment: 11 pages, 17 figures, revised version as to appear in Phys. Rev.

The electronic structure of two V-based ladder compounds, the quarter-filled NaV2O5 in the symmetric phase and the iso-structural half-filled CaV2O5, is investigated by ab initio calculations. Based on the bandstructure we determine the dielectric tensor ε(ω) of these systems in a wide energy range. The frequencies and eigenvectors of the fully symmetric Ag phonon modes and the corresponding electron-phonon and spin-phonon coupling parameters are also calculated from firstprinciples. We determine the Raman scattering intensities of the Ag phonon modes as a function of polarization and frequency of the exciting light. All results, i.e. shape and magnitude of the dielectric function, phonon frequencies and Raman intensities show very good agreement with available experimental data.

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