Reduced density-matrix functional theory: Correlation and spectroscopy.

In this work, we explore the performance of approximations to electron correlation in reduced density-matrix functional theory (RDMFT) and of approximations to the observables calculated within this theory. Our analysis focuses on the calculation of total energies, occupation numbers, removal/addition energies, and spectral functions. We use the exactly solvable Hubbard dimer at 1/4 and 1/2 fillings as test systems. This allows us to analyze the underlying physics and to elucidate the origin of the observed trends. For comparison, we also report the results of the GW approximation, where the self-energy functional is approximated, but no further hypothesis is made concerning the approximations of the observables. In particular, we focus on the atomic limit, where the two sites of the dimer are pulled apart and electrons localize on either site with equal probability, unless a small perturbation is present: this is the regime of strong electron correlation. In this limit, using the Hubbard dimer at 1/2 filling with or without a spin-symmetry-broken ground state allows us to explore how degeneracies and spin-symmetry breaking are treated in RDMFT. We find that, within the used approximations, neither in RDMFT nor in GW, the signature of strong correlation is present, when looking at the removal/addition energies and spectral function from the spin-singlet ground state, whereas both give the exact result for the spin-symmetry broken case. Moreover, we show how the spectroscopic properties change from one spin structure to the other.

Double excitations in finite systems.

Time-dependent density-functional theory (TDDFT) is widely used in the study of linear response properties of finite systems. However, there are difficulties in properly describing excited states, which have double- and higher-excitation characters, which are particularly important in molecules with an open-shell ground state. These states would be described if the exact TDDFT kernel were used; however, within the adiabatic approximation to the exchange-correlation (xc) kernel, the calculated excitation energies have a strict single-excitation character and are fewer than the real ones. A frequency-dependent xc kernel could create extra poles in the response function, which would describe states with a multiple-excitation character. We introduce a frequency-dependent xc kernel, which can reproduce, within TDDFT, double excitations in finite systems. In order to achieve this, we use the Bethe-Salpeter equation with a dynamically screened Coulomb interaction W(omega), which can describe these excitations, and from this we obtain the xc kernel. Using a two-electron model system, we show that the frequency dependence of W does indeed introduce the double excitations that are instead absent in any static approximation of the electron-hole screening.

The self-energy beyond GW: local and nonlocal vertex corrections.

It is commonly accepted that the GW approximation for the electron self-energy is successful for the description of the band structure of weakly to moderately correlated systems, whereas it will fail for strongly correlated materials. In the present work, we discuss two important aspects of this approximation: first, the "self-screening error," which is due to an incorrect treatment of induced exchange, and second, the atomic limit, in which, instead, correlation is directly responsible for the observed problem. Using the example of the removal of a particle from a box, we show that the self-screening error stems from the use of test charge-test charge screening and that it can be corrected by a two-point vertex contribution to the self-energy derived from time-dependent density functional theory (TDDFT). We explain why the addition of a particle, instead, requires the use of a different approximate vertex. This illustrates why the general vertex function, valid both for valence and conduction states, must be a three-point function. Moreover, we show that also the bad performance of GW in the atomic limit is due to the neglect of the vertex in the self-energy; in that case, the TDDFT-derived vertex correction is not sufficient in order to remove the error even qualitatively. We discuss the effects of the self-screening error as well as the atomic limit using GW for the exactly solvable two-site Hubbard model.

Ab initio calculation of optical spectra of liquids: many-body effects in the electronic excitations of water.

We present ab initio calculations of the excited state properties of liquid water in the framework of many-body Green's function formalism. Snapshots taken from molecular dynamics simulations are used as input geometries to calculate electronic and optical spectra, and the results are averaged over the different configurations. The optical absorption spectra with the inclusion of excitonic effects are calculated by solving the Bethe-Salpeter equation. The insensitivity of screening effects to a particular configuration make these calculations feasible. The resulting spectra, which are strongly modified by many-body effects, are in good agreement with experiments.

Excitonic effects on the silicon plasmon resonance.

We present an ab initio calculation of the electron energy loss spectrum of silicon including local-field, self-energy, and excitonic effects. When self-energy corrections are added to the standard random phase approximation (RPA) the line shape of the plasmon resonance worsens. The electron-hole interaction cancels this correction and improves the result both compared to the RPA and to the self-energy one, yielding very good agreement between theory and experiment provided that the mixing of interband transitions of both positive and negative frequencies is included.