Recent experimental evidence suggests the existence of three distinct V-valence states $({\mathrm{V}}^{4+},\hspace{0.5em}{\mathrm{V}}^{4.5+},$ and ${\mathrm{V}}^{5+})$ in the low-temperature phase of ${\mathrm{NaV}}_2{\mathrm{O}}_5$ in apparent discrepancy with the observed spin gap. We investigate a spin cluster model, consisting of weakly coupled, frustrated four-spin clusters aligned along the crystallographic b axis that was recently proposed to reconcile these experimental observations. We have studied the phase diagram and the magnon dispersion relation of this model using DMRG, exact diagonalization, and a cluster-operator theory. We find a spin gap for all parameter values and two distinct phases, a cluster phase and a Haldane phase. We evaluate the size of the gap and the magnon dispersion and find no parameter regime which would reproduce the experimental results. We conclude that this model is inappropriate for the low-temperature regime of ${\mathrm{NaV}}_2{\mathrm{O}}_5.$

• Received 8 February 2000

DOI:https://doi.org/10.1103/PhysRevB.62.R14617