Coherent Two-Body Correlations

Abstract

The previous chapters dealt predominantly with a mean-field description of many-fermion systems. These are all approximate and leave space for correlations beyond the mean field. Correlations naturally cover a very broad field. We will discuss here three illustrative examples. A global measure for the strength of correlations is deduced from perturbation theory: it is the ratio of the average strength of the residual two-body interaction over the typical excitation energies of the system, the latter being easily quantified by the HOMO–LUMO gap . We have learned in Chap. 3 that fermion systems very much prefer situations with a large HOMO–LUMO gap which keeps correlation effects low. We have also seen that such a favorable situation is not necessarily given from the outset.