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Local energy density functional for superfluid Fermi gases from effective field theory

Over the past two decades, many studies in the Density Functional Theory context revealed new aspects and properties of strongly correlated superfluid quantum systems in numerous configurations that can be simulated in experiments. This was made possible by the generalization of the Local Density Approximation to superfluid systems by Bulgac in [Phys. Rev. C 65, 051305, (2002), Phys. Rev. A 76, 040502, (2007)]. In the presented work, we propose an extension of the Superfluid Local Density Approximation systematically improvable and applicable to a large range of many-body quantum problems getting rid of the fitting procedures of the functional parameters. It turns out that only the knowledge of the density dependence of the quasi-particle properties, namely, the chemical potential, the effective mass, and the pairing gap function, are enough to obtain an explicit and accurate local functional of the densities without any adjustment a posteriori. This opens the way toward an Effective Field Theory formulation of the Density Functional Theory in the sense that we obtain a universal expansion of the functional parameters entering in the theory as a series in pairing gap function. Finally, we discuss possible applications of the developed approach allowing precise analysis of experimental observations. In that context, we focus our applications on the static structure properties of superfluid vortices.