Making accurate predictions for strongly correlated fermions is a long-standing theoretical challenge. A new approach is developed since 10 years: All connected Feynman diagrams are sampled efficiently up to a certain order Nmax using diagrammatic Monte Carlo algorithms. Convergence of the diagrammatic series for Nmax → ∞ was observed in several interesting situations for fermions on a lattice or frustrated spins. This convergence happens thanks to the fermionic sign, and allows a computational complexity that grows only polynomially with the inverse error . I will mostly focus on the unitary Fermi gas, a continuous-space model of non-relativistic fermions in 3 space dimensions allowing precise comparison with ultracold-atom experiments. We find that the series diverges strongly (the convergence radius is zero), and there is no small parameter in the strongly correlated regime. Nevertheless, we demonstrate that one can obtain accurate results using an appropriate resummation procedure, taking into account the large-order behavior of the series, which we obtain by an instanton approach . We also compute the momentum distribution and Tan’s contact parameter; we find that the former does not follow Fermi liquid theory, while the latter depends only weakly on temperature due to two competing effects .
 R. Rossi, N. Prokof’ev, B. Svistunov, K. Van Houcke, F. Werner, Europhys. Lett. 118,
 R. Rossi, T. Ohgoe, K. Van Houcke, F. Werner, PRL 121, 130405 (2018)
 R. Rossi, T. Ohgoe, E. Kozik, N. Prokof’ev, B. Svistunov, K. Van Houcke, F. Werner,
PRL 121, 130406 (2018)