Tackling the interplay between competing interactions in complex materials

Electron-electron interaction, electron-vibrational coupling, electron-hole correlation, and spin-orbit coupling (SOC) can give rise to exciting phenomena in the response of matter to light, especially when these interactions are of similar strength. With selected examples, I will show that treating them on equal footing by many-body perturbation theory (MBPT) allows us to achieve benchmark quality and thus in-depth understanding of complex processes and excellent agreement with experiment, even for complex crystals. While MBPT is the methodology of choice for such problems, its direct application is often hampered by the computational effort when it comes to "real" materials. Here, we proceed along two different routes. On the one hand, we have implemented approaches to speed up highly demanding calculations by up to two orders of magnitude. On the other hand, to deal with disorder or defects, we combine first-principles methodology with machine-learning techniques to predict properties such as band gaps. In terms of materials, I will focus mainly on wide-gap oxides and interfaces. I will also outline our recent progress in developing methods to tackle more complex processes like exciton-exciton and exciton-phonon coupling.