Presence of midgap states inCaV4O9

Abstract

Using exact diagonalizations of finite clusters with up to 32 sites, we study the ${\mathit{J}}_{1}$-${\mathit{J}}_{2}$ 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 ${\mathit{J}}_{2}$/${\mathit{J}}_{1}$. Besides, we show that singlet states will be present in the singlet-triplet gap if ${\mathit{J}}_{2}$/${\mathit{J}}_{1}$ is not too small (${\mathit{J}}_{2}$/${\mathit{J}}_{1}$\ensuremath{\gtrsim}0.47). We argue that this property should play a central role in determining the exchange integrals in ${\mathrm{CaV}}_{4}$${\mathrm{O}}_{9}$. \textcopyright{} 1996 The American Physical Society.