2-DIMENSIONAL XXZ MODEL GROUND-STATE PROPERTIES USING AN ANALYTIC LANCZOS EXPANSION

We develop a formalism for calculating arbitrary expectation values fo r any extensive lattice Hamiltonian system using an analytic Lanczos e xpansion, or plaquette expansion, and a recently proved exact theorem for ground-state energies. The ground-state energy, staggered magnetiz ation, and excited state gap of the two-dimensional anisotropic antife rromagnetic Heisenberg model are then calculated using this expansion for a range of anisotropy parameters, and compared to other moment-bas ed techniques, such as the t expansion, and spin-wave theory, and seri es-expansion methods. We find that far from the isotropic point all mo ment methods give essentially very similar results, but near the isotr opic point the plaquette expansion is generally better than the others .