Gutzwiller theory of electron correlation at finite temperature

The Gutzwiller's scheme is extended to finite temperature in order to study the properties of electrons in strongly correlated metals. Using the quasichemical approximation we have constructed an orthogonal set of trial functions. These have a one-to-one correspondence to the Slater determinants with Bloch states. Our scheme for constructing this set of basis functions is independent of the perturbation theory. Based on this orthogonal set, the entropy of the correlated electrons has been derived from the thermodynamic equations. It has the correct behavior in the metallic phase except in the vicinity of the metal-nonmetal phase boundary. The electron effective mass and the Pauli spin susceptibility are found to be enhanced in a way similar to the Brinkman-Rice result for a correlated ground state. The Knight shift is also enhanced but the enhancement factor is much less than that for the susceptibility. However, the electronic specific heat is enhanced only for $\frac{k_{B}T}{\Delta }\gtrsim 0.11$ ($\Delta$ is the bare bandwidth). For $\frac{k_{B}T}{\Delta }\lesssim 0.11$ we need to consider the collective excitations such as paramagnons in order to have a complete treatment of the specific heat. Using an ellipsoidal density of states we have performed model calculations for a nonmagnetic state in order to illustrate the characteristic features of the strongly correlated electron system.