Ab initio approach to density response and excitation spectra in metallic systems

In this thesis I propose a detailed discussion of the calculation of the dielectric response of metallic systems. We mainly performed simulations of Al and Na, since their near free-electron like behaviour permits also a comparison with the results of the HEG model. On the other hand, we also explored the possibility that our methods could be applied to more complex system. In this direction we performed calculation of the optical properties of ferromagnetic Fe, which includes the additional complexity of the presence of the 3d electrons. We also tried to understand if the accuracy of ab initio calculations in the case of semiconductors can be extended to metallic systems. The present thesis focuses on the frequency-dependent dielectric function є(q,ω). In the first part of this thesis we review briefly the GW and TDDFT approaches used in our calculations. We will also motivate the study of bulk metals. In the second part of this thesis the new methods developed in this work do deal with the intraband contributions will be described. We will finally analyze the obtained results. In the discussion of the GW calculations for metals, we propose a method to deal with the intraband term based on a fit of the finite-momentum screened interaction. This methods works efficiently when the plasmon pole approximation is an accurate assumption. In addition to optical adsorption, other experiments permit to access the dielectric properties of metals, including the energy-loss spectroscopy and inelastic X-ray scattering spectroscopy (IXSS). In the present thesis we performed a systematic calculation of the dynamic structure factor of Na and Al to understand the role of electronic correlation beyond the random phase approximation (RPA).We perform TDDFT simulations using several exchange and correlation kernels and including quasiparticle effects, to understand how they are important to provide a satisfactory theoretical description of the experimental measurements. TDDFT is not only able to predict loss function measurements, but also optical properties. This thesis address also that problem proposing a new method to deal with the intraband transitions, method applied to Al chosen as benchmark and to ferromagnetic Fe. In Chapter 1 we introduce the many-body problem, which is described in detail in Chapter 2, where we review the many-body perturbation theory and the GW approximation. In Chapter 3 the TDDFT and the linear response formalism are presented. We introduce the dielectric function and briefly discuss its main features in Chapter 4. In Chapter 5 we show the applications, by presenting the problem of the fictitious gap introduced by the GW corrections and by proposing a fit on the polarizability to deal with the intraband transitions. We apply finally TDDFT, by discussing the IXSS spectra of Na and of Al in Chapter 6. Optical properties are discussed in Chapter 7.