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.
Highlights
We report the spectral function obtained from a dynamical 1-GF and Σ1 is the self-energy (1-SE), namely the popular GW approximation to the 1-SE
The satellites are only well described by the static approximation to the 3-SE, as they are absent in the spectral function obtained from the static approximation to the 1-SE, while the GW approximation completely fails to reproduce the positions of the satellites and severely underestimates its amplitudes
We have shown that G3e+h which is the sum of the electron-hole-hole and electron-electron-hole parts of the three-body Green’s function, contains all the necessary information to describe the spectral function
Summary
Photoemission spectroscopy is one of the most widely used experimental techniques to study the electronic structure of materials [1]. We will study the electron-hole-hole 3-GF (G3ehh) and the electron-electron-hole 3-GF (G3eeh) which contain all the required information about photoemission and inverse photoemission spectra, respectively We note that this is a general strategy: the more information the fundamental quantity contains the less information is required in the effective potential, i.e. the self-energy in our case, to describe the relevant many-body effects. We will demonstrate how one can retrieve the 1-GF and, the spectral function (which is related to photoemission spectra), from G3ehh and G3eeh We illustrate these principles by studying the symmetric Hubbard dimer at 1/4 and 1/2 filling, for which the exact self-energy is known. We note that the three-body Green’s function has been employed to describe Auger spectra [27], to study satellite structures and the occurrence of the metal-insulator transition [28], and is related to theories that use composite fermion operators, see Ref.
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