A Comparison Between Correlated Basis Functions Method and the Density Functional Theory

Abstract

The method of correlated basis functions (CBF) has been applied to treating a wide variety of homogeneous many body systems,1–4 including liquid and solid helium, nuclear matter, and Coulomb systems. That the method could be successful for Bose and Fermi systems alike has to do with its apparent ability to sum both ring and ladder diagrams, as demonstrated in an analysis by Sim and Woo5 in 1970. In that work, the pair correlation function and ground state energy for a weakly interacting Bose gas were first calculated exactly in the perturbation theory using the formalism of Hugenholtz and Pines. The same quantities were then obtained using the CBF approach. Results from the two methods were compared order by order in powers of the density and the interaction strength. This helped determine what perturbative diagrams were summed by the CBF. Indeed, from this analysis a systematic scheme was identified that enabled us6,7 to use the Hugenholtz-Pines theory to suggest optimum three-particle and higher-order factors for correlated wave functions. Thus, diagrammatic perturbation theory and CBF became intermingled.