Gutzwiller approximation applied to inhomogeneous lattice models and solid-state systems

The plan of this thesis is as follows. Chapt. 1 is devoted to the explanation of the main theoretical tool of our work, namely the GVM and GA. After introducing their earliest formulation by Martin C. Gutzwiller, we discuss their effectiveness in describing the physics of strongly correlated conductors, emphasizing the improvements they bring in comparison with mean-field, independent-electron approximations such as HF, and their limitations with respect to more refined, though computationally more costly, methods like DMFT and VQMC. We mention how the GA was initially exploited as an approximate tool for analytical calculation of expectation values on the GVW, and how later studies proved its exactness in the limit of infinite lattice coordination. After that, we discuss its more recent multi-band formulation which, together with the mixed-basis parametrization of Gutzwiller parameter matrix, is particularly important for combining the GVM with DFT. In Chapt. 2 we present our results for the strongly correlated Hubbard lattice with broken translational invariance due to the presence of a surface (panel (a) in Fig. 1), a metal-metal or metal-insulator junction (panel (b)), or a “sandwich” of Mott insulator or strongly correlated metal between metallic leads (panel (c)). For all geometries, we show the layer dependence of the quasi-particle weight and provide approximate analytical fits for the data, together with a comparison with DMFT calculations on similar systems. In Chapt. 3, we introduce the formalism of DFT, the Kohn-Sham self-consistent equations for the functional minimization and the LDA for exchange and correlation functionals. We further discuss the performance and limitations of LDA and present the LDA+U method as a way to correct the self-interaction error of LDA. We explain the details of the GDF in Chapt. 4, and underline its similarities and differences with respect to the LDA+U functional. In the same chapter we present our data for paramagnetic and ferromagnetic bcc iron obtained through our implementation of LDA+G in the Siesta code. We show energy differences between spin-polarized and unpolarized Iron computed within LDA, GGA and LDA+G and with different basis sets. We compare the band structure, lattice parameters and magnetic moments (some sample data is shown in Table 1) obtained with these functionals, and discuss the implications of our results on the understanding of the origin of magnetism in transition metals. In the appendices we list some important results that we believed too detailed or too marginal to be presented in the main body of the thesis. Appendix A is devoted to some proofs and detailed explanations related to the GVM. In Appendix B we include all details related to the calculations on the layered geometries of Chapt. 2. In Appendix C we explain how to implement spin and orbital symmetries in the parametrization of the Gutzwiller projector, while in Appendix D we give the details of the minimization algorithm we implemented for optimizing the variational energy of the LDA+G calculation with respect to Gutzwiller parameters. Finally, Appendix E contains various topics of DFT and LDA+U that are important for the understanding of the GDF we implemented and discussed in Chapt. 4.