Fractionalized Kohn-Sham Scheme for Strongly Correlated Electrons

We propose to expand the territory of density functional theory to strongly correlated electrons by reformulating the Kohn-Sham scheme in the representation of fractionalized particles. We call it the ``KS* scheme.'' Using inhomogeneous $t$-$J$ chains as a test bed, we show that the KS* scheme with simple local density approximation is able to achieve accurate ground-state energy and density distribution comparable to the density matrix renormalization group method, while the computational complexity is much lower.