Fermionic sign problem: an exaggerated myth

Feynman diagrams are the most celebrated and powerful tool of theoretical physics usually associated with an analytic approach. I will argue that diagrammatic expansions are also an ideal numerical tool with enormous and yet to be explored potential for solving interacting fermionic systems by direct simulation of connected Feynman diagrams. Though the original series based on bare propagators and interaction vertexes are sign-alternating and often divergent one can determine the answer behind them by using appropriate series re-summation techniques, conformal mappings, asymptotic series analysis, and shifted action tools, including sequences based on the skeleton diagrams. Ultimately, the diagrammatic expansion can, in principle, be always made convergent! In this formulation, the fermionic sign problem is simply absent for regular (as opposed to random) systems because (i) the entire setup is valid in the thermodynamic limit, and (ii) convergence to the exact answer is polynomial in time. Moreover, the fermionic sign is a "blessing" because it leads to massive cancellation of high-order diagrams and ultimate convergence of the re-summed series. For illustration, I will discuss results for the Fermi-Hubbard model, the unitary Fermi gas, and the homogeneous electron gas (jellium).