Self-consistency in GW Gamma formalism leading to quasiparticle-quasiparticle couplings

Within many-body perturbation theory, Hedin's formalism offers a systematic way to iteratively compute the self-energy Sigma of any dynamically correlated interacting system, provided one can evaluate the interaction vertex Gamma exactly. This is, however, impossible, in general, for it involves the functional derivative of Sigma with respect to the Green's function. Here, we analyze the structure of this derivative, splitting it into four contributions and outlining the type of quasiparticle interactions that each of them generate. Moreover, we show how, in the implementation of self-consistency, the action of these contributions can be classified into two: A quantitative renormalization of previously included interaction terms and the inclusion of qualitatively distinct interaction terms through successive functional derivatives of Gamma itself. Implementing this latter type of self-consistency can extend the validity of perturbative approximations based on Hedin's equations toward the high interaction limit, as we show in the example of the Hubbard dimer. Our analysis also provides a unifying perspective on the perturbation theory landscape, showing how the T-matrix approach is completely contained in Hedin's formalism.

Automated summary

Hedin's formalism provides a systematic way to compute the self-energy of dynamically correlated systems, but accurately evaluating the interaction vertex remains a challenge. The structure of the derivative and its contributions are analyzed, offering insights into the implementation of self-consistency. This analysis extends the validity of perturbative approximations and unifies the landscape of perturbation theory.