Generalized Random Phase Approximation: Zero and Non-Zero Temperature Properties of an Interacting Electron Gas

Correlated systems at both zero and nonzero temperature are treated here from a novel angle using a functional method. This functional method is an extension of the usual effective potential method. Here, however the effective action is made to depend explicitly on the correlation effects that are inherent in the physics involved. This will enable us to obtain new expressions for the free energy, the specific heat and the ground state energy. The new expansion is shown to give the expected results for the homogeneous case at zero temperature. However at non-zero temperature we are able to get new sets of diagrams that have a vanishing effect at zero temperature. To lowest order these diagrams if summed properly will solve a ln T anomaly in the specific heat of an electron gas at low temperature. We are also able to show that this method provides a very clear way to extend the RPA approximation. We calculate the effect of exchange on the ring diagrams at zero temperature and show how to include some of the ladder digrams. Our results agree well with known numerical calculations. We conclude by showing that this method is in fact a variant of the time dependent density functional method and can in principle be applied to study the effects of correlation in the nonhomogeneous case.