Exact diagonalization study of charge order in the quarter-filled two-leg ladder system NaV2O5

The charge ordering transition in the layer compound NaV₂O₅ is studied by means of exact diagonalization methods for finite systems. The two-leg ladders of the V-Trellis lattice are associated with one spin variable of the vanadium 3d electron in the rung and a pseudospin variable that describes its positional degree of freedom. The charge ordering (CO) due to intersite Coulomb interactions is described by an effective Ising-like Hamiltonian for the pseudospins that are coupled to the spin fluctuations along the ladder. We employ a Lanczos algorithm on a two-dimensional lattice to compute charge (pseudospin) and spin-correlation functions and the energies of the low-lying excited states. A CO phase diagram is constructed and the effect of intraladder exchange on the CO transition is studied. It is shown that a phase with no long-range order exists between the in-line and zigzag ordered structures. We provide a finite-size scaling analysis for the spin excitation gap and also discuss the type of excitations. In addition we studied the effect of bond alternation of spin exchange and derived a scaling form for the spin gap in terms of the dimerization parameter.