Ab initio pairing gap, spectral and response functions of two-dimensional ultracold fermionic gases

We study dynamical correlations of two-dimensional (2D) Fermi atomic gases at zero temperature: pairing gap, spectral function, as well as density and spin dynamical structure factors. Building on recent exact numerical calculations of static ground-state properties of the 2D Fermi gas \footnote{H. Shi, S. Chiesa, and S. Zhang, {\em{Phys. Rev. A}} {\bf{92}}, 033603 (2015)} and methodological developments for the computation of dynamical correlation functions \footnote{E. Vitali, H. Shi, M. Qin, and S. Zhang, {\em{Phys. Rev. B}} {\bf{94}}, 085140 (2016)}, we carry out exact numerical calculations using the auxiliary-field quantum Monte Carlo (AFQMC) method which, for the attractive Fermi gas, is free of the fermion sign problem. The correlation functions are analyzed via state-of-art analytic continuation methodologies in order to infer real time dynamical properties. Dynamical correlation functions provide probes of the excitations and allow potentially direct comparisons with spectroscopy and scattering experiments.