LANCZOS CLUSTER-EXPANSION FOR NON-EXTENSIVE SYSTEMS

A cluster expansion of the Lanczos recursion for non-extensive systems is developed based on the plaquette expansion for extensive systems, in which an auxiliary scaling parameter, Omega, plays the role of volu me and introduces extensivity into the problem. Connected Hamiltonian moments of the non-extensive system are computed and introduced into t he plaquette expansion in the usual way with Omega. The extensive ener gy is calculated for increasing orders of the expansion in 1/Omega and the ground state and mass gap of the finite few body problem recovere d in the limit Omega --> infinity. This new non-perturbative method is applied to the case of N bosons interacting harmonically in one dimen sion and the ground state energy and mass gap in the vacuum sector are calculated exactly.