  Deriving accurate energy density functional is one of the central problems in
condensed matter physics, nuclear physics, and quantum chemistry. We propose a
novel method to deduce the energy density functional by combining the idea of
the functional renormalization group and the Kohn-Sham scheme in density
functional theory. The key idea is to solve the renormalization group flow for
the effective action decomposed into the mean-field part and the correlation
part. Also, we propose a simple practical method to quantify the uncertainty
associated with the truncation of the correlation part. By taking the
$\varphi^4$ theory in zero dimension as a benchmark, we demonstrate that our
method shows extremely fast convergence to the exact result even for the highly
strong coupling regime.
