Diagrammatic Analysis of the Method of Correlated Basis Functions. III. Excitation Spectrum of a Weakly Interacting Bose Gas

In the continuing effort to establish contacts between the method of correlated basis functions (CBF) and the diagrammatic perturbation theory, we carry out parallel calculations of the excitation spectrum of a weakly interacting Bose gas. The Hugenholtz—Pines (HP) theory is first used to obtain the exact liquid-structure function and the energy spectrum, each to three orders in the strength parameter $\lambda$ that characterizes the interaction between a pair of particles in the system. Next we construct sets of CBF using three different correlating factors, and in each case calculate the excitation energy of the system. The results are compared to those obtained from the HP theory. Complete agreement is found to all orders considered. In conjunction with a paper to follow, the analysis demonstrates the flexibility of the CBF method and the relative ease of application in comparison to other methods.