We leverage random phase approximation and unbiased auxiliary-field quantumMonte Carlo methods to compute dynamical correlations for a dilute homogeneoustwo-dimensional attractive Fermi gas. Our main purpose is to quantitativelystudy the collective excitations of the system to generate robust benchmarkresults and to shed light into fermionic superfluidity in the stronglycorrelated regime. In particular we are motivated by a recent paper suggestingthat the Higgs mode can be detected in the spectrum of spin fluctuations.Despite the fact that we are somewhat limited by finite-size effects, our studypinpoints indeed a clear peak in the spin channel at low momentum, but adetailed analysis suggests that such a peak, though certainly interesting, doesnot correspond to the Higgs mode. We propose a different explanation for theshape of the spin structure factor. On the other hand, our results clearly showthat the Higgs mode can be detected in the density channel at very small wavevectors, although very good resolution is necessary.
We study the out-of-equilibrium dynamics of one-dimensional quantumIsing-like systems, arising from sudden quenches of the Hamiltonian parameter$g$ driving quantum transitions between disordered and ordered phases. Inparticular, we consider quenches to values of $g$ around the critical value$g_c$, and mainly address the question whether, and how, the quantum transitionleaves traces in the evolution of the transverse and longitudinalmagnetizations during such a deep out-of-equilibrium dynamics. We shed light onthe emergence of singularities in the thermodynamic infinite-size limit, likelyrelated to the integrability of the model. Finite systems in periodic and openboundary conditions develop peculiar power-law finite-size scaling laws relatedto revival phenomena, but apparently unrelated to the quantum transition,because their main features are generally observed in quenches to genericvalues of $g$. We also investigate the effects of dissipative interactions withan environment, modeled by a Lindblad equation with local decay and pumpingdissipation operators within the quadratic fermionic model obtainable by aJordan-Wigner mapping. Dissipation tends to suppress the main features of theunitary dynamics of closed systems. We finally address the effects ofintegrability breaking, due to further lattice interactions, such as inanisotropic next-to-nearest neighbor Ising (ANNNI) models. We show that somequalitative features of the post-quench dynamics persist, in particular thedifferent behaviors when quenching to quantum ferromagnetic and paramagneticphases, and the revival phenomena due to the finite size of the system.