Dynamical vertex functions of many-electron systems

Some of the most fascinating phenomena in condensed matter physics, like the famous example of unconventional high-temperature superconductivity, still lack of a convincing theoretical description. The reason behind the difficulties of our theoretical understanding is often tightly linked to the origin of the surprising phenomena we observe: the strong interaction between the many electrons of quantum materials. In particular, in all condensed matter systems, where the repulsive interaction between the electrons is not reduced enough by screening processes, the conventional band-theory, which treats all the electrons independent of one another, is no longer valid. Hence, in such cases, theoretical physicists are faced with the challenge of solving the quantum many- electron problem in its full complexity. While last decade has already witnessed an impressive improvement in the algorithmic approaches to this problem, the treatment of an essential ingredient of the many-electron physics, i.e., the two- particle scattering processes in quantum materials is still mostly neglected or heavily approximated. In our project, we plan important steps forward with respect to the state-of-the-art approaches, not only by explicitly including the two-particle scattering processes in our many-electron calculations, but also by investigating the intrinsic features of such processes on a fundamental level. This way, we will be able, on the one hand, to significantly enhance the predictive power of our numerical simulations of transport and spectroscopic measurements in quantum materials, and, on the other hand, to unveil the subtle interplay between the different fluctuations (of electric charge, or magnetic and superconducting properties) driving the puzzling phenomena of these systems. While the foreseen algorithmic developments will be beneficial for all scientist working in the field, the knowledge gained by mastering the physics of the two-particle scattering processes might held a new, powerful key for understanding several of the most heavily debated phenomena observed in quantum materials.