A uniqueness theorem in a density-matrix functional theory

TL;DR

This paper proves a uniqueness theorem for an effective interaction in a density-matrix functional theory, establishing a fundamental principle for describing electron systems with a Hubbard-type interaction.

Contribution

It introduces a uniqueness theorem for the effective interaction in an extended Kohn-Sham framework with a Hubbard-type interaction, under non-degenerate ground state conditions.

Findings

Proves the uniqueness of the effective interaction functional.

Establishes a foundational principle for electron system modeling.

Links the interaction strength to a two-body reduced density matrix.

Abstract

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.