Correlated basis function theory for fermion systems

Abstract

A description of correlated basis function theory for Fermi systems is given with the perspective of discussing some of the recent developments and its range of applications. The actual status of variational calculations in liquid helium, strongly correlated electrons and nuclear matter is presented, by discussing the merits and limitations of the most realistic trial wave functions. Correlated basis function perturbation theory is described as a tool to go beyond variational calculations. The not-orthogonal and the newly developed orthogonal versions are discussed and compared. A brief review of the one-body Green’s function calculation in nuclear matter is presented, as one of the main applications of the orthogonal version of the perturbation theory. We describe a generalized Fermi Hyper-Netted Chain scheme, showing that it constitutes a powerful method to compute the hamiltonian and identity operator matrix elements, which enter the correlated basis theory, starting from its zeroth order or variational theory. Such scheme sums up both reducible and irreducible cluster terms, whereas the original FHNC one takes care of the irreducible terms only, and it is particularly suitable for calculations with state dependent correlations, as well as for finite systems, like nuclei and helium droplets.