The problem of many-body perturbation theory was solved in the 1940s and 50s in the form of Feynman diagrammatics, yet with the exception of only a few low order diagrams general solutions are not widely available. While there are of course many challenges to computing interactions in materials (with or without diagrams) one of the biggest issues is that numerical analytic continuation is fundamentally ill-posed.
In this talk I will present an algorithm that avoids this issue and provides a fully symbolic evaluation of arbitrary Feynman diagrams from which we can obtain essentially all experimentally relevant quantities from which I will emphasize spin susceptibilities. I will present results for model systems, such as the 2D Hubbard model, and identify the challenges that need to be overcome in order to create robust general tools for material calculations.