Assessing the Accuracy of Random Phase Approximation for Dynamical Structure Factors in Cold Atoms with Quantum Monte Carlo

Cold atomic gases provide an excellent test ground to study the exotic and counterintuitive behavior of quantum many-body physics. Of particular interest is the appearance of collective excitations in these systems, such as the Goldstone and Higgs mode. To make progress, we need to assess the robustness of the theoretical and computational techniques commonly used to study the properties of cold atoms. We exploit the fact that, in some cases, exact numerical predictions can be obtained through Quantum Monte Carlo for the dynamical properties of cold atoms. We use these predictions to assess the accuracy of the Generalized Random Phase Approximation, which is widely considered the method of choice for studying collective excitations in cold atomic Fermi gases modeled with a Fermi-Hubbard Hamiltonian. We found good agreement between the two methodologies for the dynamical properties, especially for the position of the Goldstone mode. We also explored the possibility of using a renormalized, effective potential in place of the physical potential.