Reduced Density Matrix Functional Theory at Finite Temperature: Theoretical Foundations

TL;DR

This paper develops a theoretical framework for finite-temperature reduced density matrix functional theory, establishing foundational principles and a Kohn-Sham system for describing thermal equilibrium in quantum many-body systems.

Contribution

It introduces a variational principle for the grand potential based on the one-reduced density matrix and proves the existence of a Kohn-Sham system at finite temperature.

Findings

Unique determination of equilibrium properties by the one-reduced density matrix

Existence of a Kohn-Sham system reproducing the interacting system's density matrix

A method to iteratively approximate correlation contributions to the grand potential

Abstract

We present an ab-initio approach for grand canonical ensembles in thermal equilibrium with local or nonlocal external potentials based on the one-reduced density matrix. We show that equilibrium properties of a grand canonical ensemble are determined uniquely by the eq-1RDM and establish a variational principle for the grand potential with respect to its one-reduced density matrix. We further prove the existence of a Kohn-Sham system capable of reproducing the one-reduced density matrix of an interacting system at finite temperature. Utilizing this Kohn-Sham system as an unperturbed system, we deduce a many-body approach to iteratively construct approximations to the correlation contribution of the grand potential.