Photoemission spectral functions from the three-body Green's function

TL;DR

This paper introduces a novel method using the three-body Green's function to compute photoemission spectra, aiming to improve the description of satellite features in strongly correlated materials beyond traditional approaches.

Contribution

It proposes a new approach leveraging the three-body Green's function to better capture satellite structures in spectral functions, simplifying calculations with static self-energy approximations.

Findings

Successfully applied to the Hubbard dimer with exact results

Shows satellites are present in non-interacting three-body Green's function

Demonstrates potential for improved spectral function calculations

Abstract

We present an original strategy for the calculation of direct and inverse photo-emission spectra from first principles. The main goal is to go beyond the standard Green's function approaches, such as the $GW$ method, in order to find a good description not only of the quasiparticles but also of the satellite structures, which are of particular importance in strongly correlated materials. To this end we use as a key quantity the three-body Green's function, or, more precisely, its hole-hole-electron and electron-electron-hole parts, and we show how the one-body Green's function, and hence the corresponding spectral function, can be retrieved from it. We show that, contrary to the one-body Green's function, information about satellites is already present in the non-interacting three-body Green's function. Therefore, simple approximations to the three-body self-energy, which is defined by the Dyson equation for the three-body Green's function and which contains many-body effects, can still yield accurate spectral functions. In particular, the self-energy can be chosen to be static which could simplify a self-consistent solution of the Dyson equation. We give a proof of principle of our strategy by applying it to the Hubbard dimer, for which the exact self-energy is available.