Reduced Density Matrix Functional Theory And A Reduced Formulation Of Density Functional Theory
Abstract
A mathematical framework for reduced density matrix functional theory (RDMFT) is proposed. The work is inspired by and generalizes the work by E.H.~Lieb [E.H. Lieb, Int. J. Quant. Chem. 24(1983), pp.243--277] on density-functional theory (DFT). We introduce a Banach space for density matrices with finite kinetic energy. The dual space is a rich class of single-particle potentials, i.e., Hermitian forms. The ground state energy of an -fermion system with external forces given by any such Hermitian form is expressed as the Legendre--Fenchel transform of a convex and lower semicontinuous ``universal'' reduced density matrix functional. The formalism is employed to provide a mathematical framework for density-functional theory (DFT). The main tool here is a rigorous definition of diagonals of reduced density matrices. The result is a refinement of Lieb's results on DFT applicable to a wide variety of models.
Keywords
Cite
@article{arxiv.2510.12242,
title = {Reduced Density Matrix Functional Theory And A Reduced Formulation Of Density Functional Theory},
author = {Håkon R. Fredheim and Simen Kvaal},
journal= {arXiv preprint arXiv:2510.12242},
year = {2026}
}