Dynamical BCS Theory of a Two-Dimensional Attractive Fermi Gas: Effective Interactions from Quantum Monte Carlo Calculations

The primary work presented in this paper focuses on the calculation of density–density dynamical correlations in an attractive two-dimensional Fermi gas in several physically interesting regimes, including the strongly correlated BEC–BCS crossover regime. We use state-of-the-art dynamical BCS theory, and we address the possibility to renormalize the interaction strength, using unbiased Quantum Monte Carlo results as an asset to validate the predictions. We propose that a suitable interplay between dynamical BCS theory, which is computationally very cheap and yields results directly in real time domain, and Quantum Monte Carlo methods, which are exact but way more demanding and limited to imaginary time domain, can be a very promising idea to study dynamics in many-body systems. We illustrate the idea and provide quantitative results for a few values of the interaction strength in the cold gas.