Diagrammatic Analysis of the Method of Correlated Basis Functions

Abstract

The weakly interacting Bose gas is studied on the one hand with the independent-particle perturbation formalism of Hugenholtz and Pines, and on the other hand by a perturbation theory using a set of correlated basis functions. We find by comparison that up to fourth order in energy, a Jastrow correlated wave function sums all rings and ladders, and other diagrams in part; and the simplest correlated basis functions perturbation correction accounts for all remaining discrepancies.