Simple variational wave functions for two-dimensional heisenberg spin-antiferromagnets

We generalize a type of variational wave function introduced by Kasteleijn and Marshall, to include long-range correlations and nonbipartite lattices. We find the lowest-energy wave function in a three-parameter space for both the square- and triangular-lattice spin- Heisenberg antiferromagnets. This produces useful upper bounds on the ground-state energies of these systems. The wave functions are completely explicit, so that precise estimates of expectation values are readily obtained by Monte Carlo techniques. It appears that the antiferromagnet has long-range magnetic order on the triangular lattice, as well as on the square lattice.