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In nuclear physics, Density Functional Theory (DFT) provides the basis forstate-of-the art studies of ground-state properties of heavy nuclei. However,the direct relation of the density functional underlying these calculations andthe microscopic nuclear forces is not yet fully understood. We present acombination of DFT and Renormalization Group (RG) techniques which allows tostudy selfbound many-body systems from microscopic interactions. We discuss itsapplication with the aid of systems of identical fermions interacting via along-range attractive and short-range repulsive two-body force in onedimension. We compute ground-state energies, intrinsic densities, and densitycorrelation functions of these systems and compare our results to thoseobtained from other methods. In particular, we show how energies of excitedstates as well as the absolute square of the ground-state wave function can beextracted from the correlation functions within our approach. The relationbetween many-body perturbation theory and our DFT-RG approach is discussed andillustrated with the aid of the calculation of the second-order energycorrection for a system of $N$ identical fermions interacting via a generaltwo-body interaction. Moreover, we discuss the control of spuriously emergingfermion self-interactions in DFT studies within our framework. In general, ourapproach may help to guide the development of energy functionals for futurequantitative DFT studies of heavy nuclei from microscopic interactions.

Formation of Selfbound States in a One-Dimensional Nuclear Model -- A Renormalization Group based Density Functional Study