Abstract

I will discuss two different Diagrammatic Monte Carlo schemes for solving the problem of the BCS -BEC crossover in a Fermi gas with resonant attractive interactions (the so-called zero-range universal limit). One is based on summation of relevant Feynman diagrams for the partition function of up to several hundred fermions. We determine the normal-superfluid transition temperature in the BCS -BEC crossover region, unambiguously confirm that the maximum of T_c is on the Bose side, and at unitarity T_c/E_F=0.152(7). The other scheme is based on direct summation of Feynman diagram for the proper self-energy. This approach is used to solve the problem of a single spin-down fermion resonantly interacting with the Fermi gas of spin-up particles. Though the original series based on bare propagators are sign-alternating and often divergent one can still determine the answer behind them by using two strategies (separately or together): (i) using proper series re-summation techniques, and (ii) introducing renormalized propagators which are defined in terms of the simulated proper self-energy, i.e. making the entire scheme self-consistent. Our solution is important for understanding the phase diagram and properties of the BCS -BEC crossover in the strongly imbalanced regime. On the technical side, we develop a generic sign-problem tolerant method for exact numerical solution of the interacting many-body Hamiltonians.