The multi-channel Dyson equation: coupling many-body Green’s functions. – (Gabriele Riva / LCPQ / Thèse). – 24/10/2023, 13H30

Soutenance de thèse

Gabriele Riva, LCPQ, Salle de Conférence FERMI 3R4

Summary :
In this thesis we concentrate on the ab-initio theoretical description of photoemission and optical spectroscopy. These two techniques are valuable tools to get information about the electronic structure, which is the cornerstone of our understanding of material properties. We present the multi-channel Dyson equation that combines two or more many-body Green’s functions to describe the electronic structure of materials. First, we use it to model photoemission spectra by coupling the one-body Green’s function with the three-body Green’s function.

We demonstrate that, unlike methods using only the one-body Green’s function, our approach puts the description of quasiparticles and satellites on an equal footing. We propose a multi-channel self-energy that is static and only contains the bare Coulomb interaction, making frequency convolutions and self-consistency unnecessary. Despite its simplicity, we demonstrate with a diagrammatic analysis that the physics it describes is extremely rich. We then use our new framework to model absorption spectra by coupling the two-body Green’s function with the four-body Green’s function. Also in this case the corresponding multi-channel self-energy is static and yet it contains a rich physics. This approach should be able to give a more complete description of absorption, by naturally including also double excitations. We finally apply the multi-channel Dyson equation that couples the one-body and three-body channels to the Hubbard dimer and show that it is exact both at 1/4 and 1/2 filling.