Construction of energy density functional for arbitrary spin polarization using functional renormalization group

We show an application of the functional-renormalization-group aided density functional theory to homogeneous electron gas with arbitrary spin polarization, which gives energy in local approximation. The correlation per particle is calculated at Wigner-Seitz radius $ r_{\rm s} and polarization \zeta $. In high-density region, our result shows good agreement Monte Carlo (MC) data. MC data better case small while discrepancy increases as increases. magnetic properties given by numerical results are also discussed.