Some New Variational Resonating-Valence-Bond-Type Wave Functions for the Spin-½ Antiferromagnetic Heisenberg Model on a Square Lattice

We consider a class of singlet resonanting-valence-bond wave functions on a square lattice, with the bond-length distribution as a variational parameter. This class contains the two limiting cases of the dimer wave function and of the N\'eel state. We present numerical calculations of the energy and the spin-spin correlation functions up to very large lattice sizes (180×{}180) both for disordered states with exponentially decaying correlation functions and for ordered states. The energy of a disordered state can be within 0.1% of our best ordered state (-0.3344Jbond).