Sign rules for anisotropic quantum spin systems

We present exact "sign rules" for various spin-a anisotropic spin-lattice m odels. It is shown that, after a simple transformation which utilizes these sign rules, the ground-state wave function of the transformed Hamiltonian is positive definite. Using these results exact statements for various expe ctation values of off-diagonal operators are presented, and transitions in the behavior of these expectation values are observed at particular values of the anisotropy. Furthermore, the importance of such sign rules in variat ional calculations and quantum Monte Carlo calculations is emphasized. This is illustrated by a simple variational treatment of a one-dimensional anis otropic spin model.