Nearest-neighbor resonating-valence-bond state in two dimensions

The ground state of the spin-½ Heisenberg model with antiferromagnetic coupling on a square lattice is analyzed in terms of nearest-neighbor resonating pair-bond states. Extrapolating from finite lattice calculations it is found that the pair-bond state provides a much closer variational estimate of the ground-state energy than the widely used Gutzwiller wave function. The effect of an orthorhombic distortion of the square lattice, such as that observed in the Cu-O planes in the high-$T_c$ oxides, on the spin state is analyzed by exact calculation for finite lattices. From total-energy considerations it is found that the system has a slight tendency towards such a lattice distortion.