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 s pin 1/2 isotropic XY chain in the thermodynamic limit, yielding a form for the Lanczos coefficient beta(2)(s). This coefficient has a monotonic variat ion for real positive s and confirms a general theorem on the ground state properties of extensive many-body systems. The Taylor expansion of the coef ficient about s = 0 has a finite radius of convergence, and ground state es timates based on a finite truncation of this are shown to be asymptotic. (C ) 1999 Elsevier Science B.V.