---
abstract: 'The grand potential of a system of interacting electrons is considered as a stationary point of a self-energy functional. It is shown that a rigorous evaluation of the functional is possible for self-energies that are representable within a certain reference system. The variational scheme allows to construct new non-perturbative and thermodynamically consistent approximations. Numerical results illustrate the practicability of the method.'
author:
- 'Michael Potthoff [@ad]'
title: 'Self-energy-functional approach to systems of correlated electrons'
---

Introduction {#sec:intro}
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Systems of strongly correlated electrons continue to represent a central subject of current research. Different interesting correlation phenomena, such as high-temperature superconductivity, [@OM00] Mott metal-insulator transitions [@Geb97] or itinerant ferromagnetism, [@BDN01] are far from being finally clarified. Progress in this field crucially depends on the development of new theoretical methods as even highly idealized model systems pose notoriously difficult problems. There are only a few general approaches which are able to access the equilibrium thermodynamics as well as excitation properties of an extended system of correlated electrons.

General methods can be based on the Green’s-function formalism of Luttinger and Ward [@LW60] and Baym and Kadanoff: [@BK61] Here the grand potential $\Omega$ is expressed in terms of the time- or frequency-dependent 