Electron correlation in metals: Density matrix approach

Abstract

The conceptual simplicity gained by the use of density matrices to describe the ground state of an electron gas moving in the field of a uniform background of positive charge (Sommerfeld model of a metal) is stressed. The diagonal element of the second-order density matrix (pair function) for a low-density electron gas has been discussed, previously byMarch andYoung [1], and it is shown, here that, to a similar degree of approximation, the first-order matrix and hence the momentum distribution may be obtained. In the high-density limit, where perturbation theory is valid,Daniel andVosko [2] have recently discussed the way in which the momentum distribution develops from the Fermi froms as the density is lowered (or the interaction switched on). A calculation which yields the pair function to the same degree of approximation is reported here, the results being obtained using Green’s functions, which are closely related to density matrices. In the light of the information thus available from the high and low density limits, the range of usefulness of the concept of the Fermi surface in an interacting electron gas is briefly discussed.