Non-perturbative construction of the Luttinger-Ward functional

TL;DR

This paper presents a non-perturbative derivation of the Luttinger-Ward functional using a functional-integral approach, highlighting its universality beyond weak-coupling approximations.

Contribution

It introduces a non-perturbative, functional-integral method to construct the Luttinger-Ward functional, extending its applicability to a broader class of models.

Findings

Luttinger-Ward functional can be derived non-perturbatively.

The approach emphasizes the universality of the functional.

The method applies to a large class of correlated electron models.

Abstract

For a system of correlated electrons, the Luttinger-Ward functional provides a link between static thermodynamic quantities on the one hand and single-particle excitations on the other. The functional is useful to derive several general properties of the system as well as for the formulation of thermodynamically consistent approximations. Its original construction, however, is perturbative as it is based on the weak-coupling skeleton-diagram expansion. Here, it is shown that the Luttinger-Ward functional can be derived within a general functional-integral approach. This alternative and non-perturbative approach stresses the fact that the Luttinger-Ward functional is universal for a large class of models.