Density-functional theory with adaptive pair density: The Gutzwiller approximation as a density functional

We propose a density functional to find the ground state energy and density of interacting particles, where both the density and the pair density can adjust in the presence of an inhomogeneous potential. As a proof of principle we formulate an a priori exact functional for the inhomogeneous Hubbard model. The functional has the same form as the Gutzwiller approximation but with an unknown kinetic energy reduction factor. An approximation to the functional based on the exact solution of the uniform problem leads to a substantial improvement over the local density approximation.