ACCURATE CALCULATION OF GROUND-STATE ENERGIES IN AN ANALYTIC LANCZOS EXPANSION

An analysis of a general non-perturbative technique for calculating gr ound-state properties of extensive lattice many-body systems is presen ted, in order to extract accurate numerical values characterizing the ground-state spectrum. This technique, the plaquette expansion, employ s 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 met hod and the truncation in the plaquette expansion, allows for an accur ate estimate when the approximation is taken to a given order. As an e xample we analyse the one-dimensional antiferromagnetic Heisenberg mod el, and find that the best groundstate energy density is within 3 x 10 (-6) of the exact value, although the systematic error is 10(-5) We al so find, for this model, systematic improvement with each new order in cluded in the expansion and have not observed any asymptotic tendencie s. At equivalent orders of truncation we achieve far better results th an for the other moment methods, such as the t-expansion or the connec ted-moment expansion.