One-particle irreducible functional approach: A route to diagrammatic extensions of the dynamical mean-field theory

We present an approach which is based on the one-particle irreducible (1PI) generating functional formalism and includes electronic correlations on all length scales beyond the local correlations of dynamical mean-field theory (DMFT). This formalism allows us to unify aspects of the dynamical vertex approximation (D Gamma A) and the dual fermion (DF) scheme, yielding a consistent formulation of nonlocal correlations at the one-and two-particle level beyond DMFT within the functional integral formalism. In particular, the considered approach includes one-particle reducible contributions from the three-and more-particle vertices in the dual fermion approach, as well as some diagrams not included in the ladder version of D Gamma A. To demonstrate the applicability and physical content of the 1PI approach, we compare the diagrammatics of 1PI, DF, and D Gamma A, as well as the numerical results of these approaches for the half-filled Hubbard model in two dimensions.