Density-matrix functionals from Greens functions

TL;DR

This paper establishes a formal connection between Green's function methods and density-matrix functionals, enabling new approximations and a true minimum principle for strongly correlated systems.

Contribution

It derives the exact reduced density-matrix functional from the Luttinger-Ward functional, linking diagrammatic many-body approaches with wave-function theories.

Findings

Provides a convex density-matrix functional with a true minimum principle.

Enables construction of approximations equivalent to diagrammatic resummation techniques.

Discusses applications to geometrical optimization of strongly correlated materials.

Abstract

The exact reduced density-matrix functional is derived from the Luttinger-Ward functional of the single-particle Green's function. Thereby, a formal link is provided between diagrammatic many-body approaches using Green's functions on the one hand and theories based on many-body wave functions on the other. This link can be used to explicitly construct approximations for the density-matrix functional that are equivalent to standard diagrammatic re-summation techniques and to non-perturbative dynamical mean-field theory in particular. Contrary to functionals of the Green's-function, the exact density-matrix functional is convex and thus provides a true minimum principle which facilitates the calculation of the grand potential and derived equilibrium properties. The benefits of the proposed Green's-function-based density-matrix functional theory for geometrical structure optimization of strongly correlated materials are discussed.