Accurate calculation of ground state energies in an analytic Lanczos expansion

An analysis of a general non-perturbative technique for calculating ground state properties of extensive lattice many-body systems is presented, in order to extract accurate numerical values characterising the ground state spectrum. This technique, the plaquette expansion, employs an expansion about the thermodynamic limit of the coefficients that are generated by the Lanczos process. For the ground state energy this error analysis, using theorems on the error bounds for the Lanczos method and the truncation in the plaquette expansion, allows for an accurate estimate when the approximation is taken to a given order. The 1-dimensional antiferromagnetic Heisenberg model, was analysed and found the best ground state energy density is within 3 x 10-6 of the exact value, although the systematic error is 10-5. Systematic improvement was found for this model with each new order included in the expansion and have not observed any asymptotic tendencies. It was estimated that at equivalent orders of truncation, this method gave far better results than the other moment methods, such as the t-expansion or the connected moment expansion. (authors). 22 refs., 2 tabs., 4 figs