Resonating-Valence-Bond Ground-state of CaV$_4$O$_9$ by the   Gutzwiller-projected Schwinger-boson method
  An antiferromagnetic Heisenberg model on a 1/5-depleted two-dimensional square-lattice, a model of CaV$_4$O$_9$, is investigated by variational Monte Carlo simulation. A prototype of a trial wave function is made by projecting out the doubly occupied states from the Schwinger-boson mean-field solution. Then variational Monte Carlo simulation is performed up to $40 \times 40 $ sites(including $320$ vacant sites). The optimized state has the lowest energy, $-0.5510J$, ever reported. For this state energies of a dimer bond and a plaquette bond, staggered magnetization, static structure factor, and excitation spectrum are calculated. It is shown that the N\'eel order survives and there is no gap at isotropic coupling. 
T. Miyazaki and D. Yoshioka