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

Abstract 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 β 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.