Electron correlation in metals: Density matrix approach

The conceptual simplicity gained using 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 is considered; to a similar degree of approximation, the first-order matrix and hence the momentum distribution may be obtained. In the highdensity limit, where perturbation theory is valid, Daniel and Yosko (Phys. Rev., 120: 2041(1960)) discussed the way in which the momentum distribution develops from the Fermi forms as the density is lowered (or the interaction switched on). A calculation yielding the pair function to the same degree of approximation is reported, the results being obtained using Green's functions, which are closely related to density matrices. The range of usefulness of the concept of the Fermi surface in an interacting electron gas is discussed. (auth)