The exact realisation of the Lanczos Method for a quantum Many-Body System

The Lanczos process has been analytically and exactly carried out for the spin 1/2 isotropic XY chain in the thermodynamic limit, yielding a form for the Lanczos coefficient $\beta^2(s)$. This coefficient has a monotonic variation for real positive $s$ and confirms a general theorem on the ground state properties of extensive Many-body Systems. The Taylor expansion of the coefficient about s=0 has a finite radius of convergence, and ground state estimates based on a finite truncation of this are shown to be asymptotic.