Multichannel Dyson equations for even- and odd-order Green's functions: application to double excitations

TL;DR

This paper develops a multichannel Dyson equation framework for higher-order Green's functions, enabling accurate modeling of complex many-body excitations like biexcitons and double excitations, with applications to spectroscopies.

Contribution

It extends the multichannel Dyson equation to higher-order Green's functions and demonstrates its effectiveness in describing complex excitations such as double excitations.

Findings

Accurately describes single and double excitations in a two-level model

Provides a systematic approach to approximate multichannel self-energy

Shows good agreement with exact results for complex excitations

Abstract

We extend the concept of the multichannel Dyson equation that we have recently derived to model photoemission spectra by coupling the one- and the three-body Green's functions, to higher-order Green's functions and to other spectroscopies. We show the general structure of the equations and how one can systematically approximate the corresponding multichannel self-energy. As a particular case, we focus on the coupling of the two-body and the four-body Green's functions in the electron-hole channel to describe neutral excitations. This formulation allows for the description of important many-body effects, such biexcitons, in a natural way. We illustrate our approach by applying it to a two-level model system, which, in a one-particle picture, exhibits single and double excitations. Our method can correctly describe both kinds of excitation, unlike standard approaches, and in good agreement with the exact results.