Renormalization group approach to density functional theory

We study specific types of 1+1-dimensional field theories which allow us to study the ground-state properties of self-bound systems of spinless fermions which can also be viewed as toy models of nuclei. To this end, we apply our recently developed renormalization group (RG) approach to Density Functional Theory (DFT) to these systems. Our approach indeed relates to conventional DFT in a simple manner and can in principle be used to study ground-state properties of non-relativistic many-body systems from microscopic interactions. Although the basic RG equation underlying our approach is exact, its solution requires approximations. To construct the latter, we employ the exact solution for the two-body system. In this talk, we present our results for ground-state properties, such as ground-state energies, densities, and pair-correlation functions, from this RG approach to DFT for self-bound systems with many fermions interacting via a short-range repulsive and long-range attractive interaction.