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We show an $\textit{ab initio}$ construction of the energy density functional(EDF) for electron systems using the functional renormalization group. Thecorrelation energies of the homogeneous electron gas given in our frameworkreproduce the exact behavior at high density and agree with the Monte-Carlodata in a wide range of densities. Our analytic technique enables us to get thecorrelation energies efficiently for various densities, which realizes thedetermination of EDF in the local density approximation (LDA) without anyfitting for physically relevant densities. Applied to the Kohn-Sham calculationfor the noble gas atoms, our EDF shows comparable results to those of otherconventional ones in LDA.

physical review research

Ab initio construction of the energy density functional for electron  systems with the functional-renormalization-group-aided density functional  theory