Recently, a new method, based on stochastic integration on the surfaces of steepest descent of the action, was introduced to tackle the sign problem in quantum field theories. We show how this method can be used in many body theories to perform fully non-perturbative calculations of quantum corrections about mean field solutions. We discuss an explicit algorithm for implementing our method, and present results for the repulsive Hubbard model away from half-filling at intermediate temperatures. Our results are consistent with those from the recent state of the art cluster dynamical mean field theory calculations.

In these proceedings, we summarize the Lefschetz thimble approach to the sign problem of Quantum Field Theories. In particular, we review its motivations, and we summarize the results of the application of two different algorithms to two test models.