We generalized the Gutzwiller projectional variational method for the ground state of strongly correlated electron systems to the case of finite temperature. Under the Gutzwiller approximation, we show that this maps to a finite temperature renormalized mean-field theory. As one of the key ingredients in the theory, we obtained an explicit expression of the projection entropy or the entropy change due to the projection. We illustrate the application of the theory to the Anderson impurity problem and the half-filled Hubbard model and compare the theory to more elaborate techniques. We find qualitative agreement. The theory can be applied to a wide variety of Hubbard, $t\text{\ensuremath{-}}J$, and Anderson impurity models.
Degenerate Hubbard models are studied using the Generalized-Gutzwiller-Approximation. It is found that the metal-insulator transition occurs at a finite correlation Uc when the average number of electrons per lattice site is an integer. The critical Uc depends sensitively on both the band degeneracy N and the filling x. A derivation is presented for the general expression of Uc(x,N) which reproduces all previously known Gutzwiller solutions, including that of the Boson Hubbard model. Effects of the lattice structure on the metal-insulator transition and the effective mass are discussed. PACS numbers: 71.10.+x,71.30.+h,74.70.W Typeset using REVTEX 1 The simple Hubbard model, where each lattice site is occupied by at most two electrons, has been extensively studied in recent years as a model of strongly correlated electron systems. 1,2 But in many systems, such as molecular solids C60 and AxC60, 3 the conduction band is degenerate which allows the occupation of more than two electrons per lattice site. For these systems, studying the degenerate Hubbard model on a lattice is the first step toward the understanding of electron-electronic correlations. Yet, there has been little progress since the pioneering works of Chao and Gutzwiller in early 1970s. 4 Recently, we succeeded in obtaining the Gutzwiller-like analytical solutions to degenerate Hubbard models using a scheme similar to the original Gutzwiller-Approximation. 5 A brief report of our results has been published. 6 The solution was used successfully to interpret the unusual metal-insulator transitions observed in fullerides AxC60. 6,7 In this paper we present details of our derivation and the approximation. In addition, effects of the crystal lattice structure on the metal-insulator transition and the effective mass are also investigated. We consider the N-fold degenerate Hubbard model defined on a lattice
Within the time-dependent Gutzwiller approximation applied to one-dimensional Holstein and Su-Schrieffer-Heeger-Hubbard models, we study the influence of electron correlations on the phonon self-energy. For the local Holstein coupling, we find that the phonon-frequency renormalization gets weakened upon increasing the on-site interaction
U for all momenta. In contrast, correlations can enhance the phonon-frequency shift for small wave vectors in the Su-Schrieffer-Heeger-Hubbard model. Moreover, the time-dependent Gutzwiller approximation applied to the latter model provides a mechanism which leads to phonon-frequency corrections at intermediate momenta due to the coupling with double-occupancy fluctuations. Both models display a shift of the nesting induced to a
q=0 instability when the on-site interaction becomes sufficiently strong and thus establishing phase separation as a generic phenomenon of strongly correlated electron-phonon coupled systems.