A uniqueness theorem in a density-matrix functional theory

Uniqueness of effective interaction defined in an extension of the Kohn-Sham theory is proved, if the model with a non-degenerate ground state exists and to reproduce a correlation function as well as the single-particle density of an electron system. The two-body interaction term is regarded as a Hubbard-type short range interaction term. The interaction strength is a functional of an element of a two-body reduced density matrix of the electron system. The uniqueness theorem gives a basic principle for effective description of electron systems.