The multi-channel Dyson equation: coupling many-body Green's functions

TL;DR

This paper introduces a multi-channel Dyson equation that couples multiple Green's functions to improve the modeling of electronic spectra, capturing quasiparticles and satellites more accurately with a simplified, static self-energy approach.

Contribution

It proposes a novel multi-channel Dyson equation framework coupling Green's functions, enabling accurate spectral modeling with a static self-energy and a versatile effective Hamiltonian.

Findings

Accurately models photoemission spectra including satellites.

Exact results for Hubbard dimer at specific fillings.

Simplifies computations by avoiding frequency convolutions.

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.