Quantum many-body theories, including diagrammatic perturbation theory and non-perturbative embedding theories, are rigorous and well-developed theories used to describe the physics of many interacting particles in solids. They are typically applied to lattice model systems that capture only the essential degrees of freedom.
This talk will summarize recent progress on solving the many-body problem ab-initio, i.e. without adjustable parameters and without the construction of effective low-energy models, using diagrammatic and embedding theories. We will show how algorithmic and computational advances have enabled the adaptation of tools that were previously only available on lattice models to real-materials simulations, and how these simulations now avoid several common uncontrolled approximations. A path towards controlled and adaptive many-body simulations is outlined.