Charge order induced by electron-lattice interaction in Na V2 O5

We present density matrix renormalization group calculations of the ground-state properties of quarter-filled ladders including static electron-lattice coupling. Isolated ladders and two coupled ladders are considered, with model parameters obtained from band-structure calculations for α′−NaV2O5. The relevant Holstein coupling to the lattice causes static out-of-plane lattice distortions, which appear concurrently with a charge-ordered state and which exhibit the same zigzag pattern observed in experiments. The inclusion of electron-lattice coupling drastically reduces the critical nearest-neighbor Coulomb repulsion Vc needed to obtain the charge-ordered state. No spin gap is present in the ordered phase. The charge ordering is driven by the Coulomb repulsion and the electron-lattice interaction. With electron-lattice interaction, coupling two ladders has virtually no effect on Vc or on the characteristics of the charge-ordered phase. At V=0.46eV, a value consistent with previous estimates, the lattice distortion, charge gap, charge-order parameter, and the effective spin coupling are in good agreement with experimental data for NaV2O5.