Density-matrix functionals from Greens functions

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.

15 pages

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• Iterative subspace algorithms for finite-temperature solution of Dyson equation
• Evaluation of two-particle properties within finite-temperature self-consistent one-particle Green's function methods: theory and application to GW and GF2
• Gutzwiller Density Functional Theory: a formal derivation and application to ferromagnetic nickel
• Hohenberg-Kohn theorems for interactions, spin and temperature
• Approximate energy functionals for one-body reduced density matrix functional theory from many-body perturbation theory
• Realistic many-body approaches to materials with strong nonlocal correlations
• Theoretical Study of Ternary CoSP Semiconductor: a Candidate for Photovoltaic Applications
• Electronic and magnetic properties of transition-metal doped ScN for spintronics applications
• Off-shell effective energy theory: a unified treatment of the Hubbard model from d=1 to d=$\infty$
• Inverse Mean Field Theory
• Variational structure of Luttinger-Ward formalism and bold diagrammatic expansion for Euclidean lattice field theory
• Bold Feynman diagrams and the Luttinger-Ward formalism via Gibbs measures. Part II: Non-perturbative analysis