  The charge ordering transition in the layer compound NaV2O5 is studied by
means of exact diagonalization methods for finite systems. The 2-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
pseudo-spins that are coupled to the spin fluctuations along the ladder. We
employ a Lanczos algortihm on 2D lattice to compute charge (pseudo-spin) and
spin-correlation functions and the energies of the low lying excited states. A
CO-phase diagram is constructed and the effect of intra-ladder exchange on the
CO transition is studied. It is shown that a phase with no-longe range order
(no-LRO) exists between the in-line and zig-zag 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.
