Spectrum of density and spin density fluctuations of an attractive two-dimensional Fermi gas

We leverage unbiased auxiliary-field quantum Monte Carlo methods interfaced with cutting-edge analytic continuation tools to compute from first-principles dynamical correlations for a dilute homogeneous two-dimensional attractive Fermi gas. Our main purpose is to quantitatively study the collective excitations of the system to shed light into fermionic superfluidity in the strongly correlated regime. Despite the fact that we are somewhat limited by finite-size effects, our study pinpoints a clear peak in the spin channel at low momentum, and we discuss the possibility that such a peak can be interpreted as the Higgs mode in the superfluid. Our study is complemented by a systematic comparison with the predictions of generalized random phase approximation, with the dual purpose to directly compare with auxiliary-field quantum Monte Carlo and to quantitatively study finite-size effects.