PHOTOEMISSION FROM THE 3-BODY GREEN’S FUNCTION

Work package:
Spectroscopy is an important experimental technique to understand the electronic structure of molecules and solids. Many-body perturbation theory (MBPT) based on Green’s functions is an important tool to de- scribe and understand various spectroscopies [1,2]. Traditionally, MBPT is limited to the one-body Green’s function (G1), which describes the propagation of a single particle (in a molecule or solid), and the two-body Green’s function G2, which describes the simultaneous propagation of two particles. The interaction with all the other particles of the system is hidden in an effective potential called the self-energy which has to be approximated in practice. From G1 and G2 we in principle describe photoemission (see figure) and absorption spectroscopy. However, accurate approximations to the self-energy are needed to accurately describe all the physics. In particular, so-called satellite features are difficult to describe in photoemission spec- tra since they are related to the interaction between a photohole (what remains after an electron is emitted) and electron-hole pairs. Therefore, we have recently started to study the three-body Green’s function (G3) as the key variable since it describes three particles simultaneously. Therefore, the interaction of a photohole with electron- hole pairs can be treated explicitly and we can use simple approximations to the self-energy to obtain the photoemission spectrum. We have recently successfully applied our approach to the symmetric Hubbard dimer which is a simple model that is similar to the hydrogen molecule. During this internship the student will test our method on more elaborate models such as the one- dimensional Hubbard chain and/or on real molecules and solids. The developments performed during the internship can be both analytical, which requires a good background in mathematics, and/or numerical, in which case some programming skills are desirable.