Diagrammatic Monte Carlo for attractively interacting fermions

A major long-standing goal is the precise computation of properties of interacting many-fermion systems. By evaluating connected Feynman diagrams, the diagrammatic Monte Carlo approach works directly for infinite system size. Thanks to efficient Monte Carlo algorithms, one can reach high enough orders to observe convergence up to a small error bar, provided the diagrammatic series is sufficiently well behaved, if necessary after applying a divergent-series resummation procedure. A crucial ingredient is to use dressed propagators or vertices as building blocks of the diagrams, and to expand around an appropriate starting point. The functional integral formalism allows to justify the validity of such reorganized expansions and their resummability, even for a zero convergence radius. I will present results for two cases of experimental relevance: The normal phase of the unitary Fermi gas, and the superfluid phase of the attractive Hubbard model.