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

DOI:https://doi.org/10.1103/PhysRevB.55.10412