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We present an original strategy for the calculation of direct and inversephoto-emission spectra from first principles. The main goal is to go beyond thestandard Green's function approaches, such as the $GW$ method, in order to finda good description not only of the quasiparticles but also of the satellitestructures, which are of particular importance in strongly correlatedmaterials. To this end we use as a key quantity the three-body Green'sfunction, or, more precisely, its hole-hole-electron and electron-electron-holeparts, and we show how the one-body Green's function, and hence thecorresponding spectral function, can be retrieved from it. We show that,contrary to the one-body Green's function, information about satellites isalready present in the non-interacting three-body Green's function. Therefore,simple approximations to the three-body self-energy, which is defined by theDyson equation for the three-body Green's function and which contains many-bodyeffects, can still yield accurate spectral functions. In particular, theself-energy can be chosen to be static which could simplify a self-consistentsolution of the Dyson equation. We give a proof of principle of our strategy byapplying it to the Hubbard dimer, for which the exact self-energy is available.

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