Simple Variational Wavefunctions for Two-Dimensional Heisenberg Spin-1/2 Antiferromagnets.

We generalize a type of variational wavefunction introduced by Kasteleijn and Marshall, to include long-range correlations and non-bipartite lattices. We find the lowest energy wavefunction in a 3-parameter space for both the square and triangular lattice spin-1/2 Heisenberg antiferromagnets. This produces useful upper bounds on the ground-state energies of these systems. The wavefunctions are completely explicit, so that precise estimates of expectation values are readily obtained using Monte Carlo techniques. It appears that the antiferromagnet has long-range magnetic order on the triangular lattice, as well as the square lattice.