The multi-channel Dyson equation: coupling many-body Green's functions
Abstract
We present the multi-channel Dyson equation that combines two or more many-body Green's functions to describe the electronic structure of materials. In this work 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. Finally, we present a framework based on an effective Hamiltonian that can be solved for any many-body system using standard numerical tools. We illustrate our approach by applying it to the Hubbard dimer and show that it is exact both at 1/4 and 1/2 filling.
Cite
@article{arxiv.2310.01204,
title = {The multi-channel Dyson equation: coupling many-body Green's functions},
author = {Gabriele Riva and Pina Romaniello and J. Arjan Berger},
journal= {arXiv preprint arXiv:2310.01204},
year = {2023}
}