The Hubbard Model from a Diagrammatic Monte Carlo Perspective

In this talk I will introduce the Diagrammatic Monte Carlo approach for strongly correlated systems and illustrate how one can use perturbation theory to obtain results in non-perturbative regimes. I will showcase recent state-of-the-art results obtained for the two- and three-dimensional Fermi-Hubbard model in the paramagnetic as well as symmetry broken phases. In particular, I will discuss the various crossovers found in the half-filled two-dimensional model as well as their relation to the more intricate pseudogap physics found upon doping and/or the addition of next-nearest-neighbor hopping terms.