Presence of midgap states in CaV4O9

Using exact diagonalizations of finite clusters with up to 32 sites, we study the J(1)-J(2) model on the 1/5 depleted square lattice. Spin-spin correlation functions are consistent with plaquette order in the spin gap phase which exists for intermediate values of J(2)/J(1). Besides, we show that singlet states will be present in the singlet-triplet gap if J(2)/J(1) is not too small (J(2)/J(1) greater than or similar to 0.47). We argue that this property should play a central role in determining the exchange integrals in CaV4O9.