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arXiv · 2610.08512

Dynamical vertex approximation for retarded interactions: Application to the Hubbard-Holstein model

Emin Moghadas·Samuele Giuli·Massimo Capone·Alessandro Toschi
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Abstract

We extend the dynamical vertex approximation (D$Γ$A), in its most commonly used ladder-version, to systems with retarded electronic interactions. Such an extended scheme, which we name "dynamical-$U$ D$Γ$A", allows us to study strongly interacting electrons coupled to bosons including non-local spatial correlations on all length scales on top of the purely local ones captured by dynamical mean-field theory. We demonstrate the applicability of the method in the specific case of the coupling to a single dispersionless phononic mode, by studying the Hubbard-Holstein model on the square and cubic lattices, focusing on regimes of sizable Hubbard interactions where strong electronic correlations compete with phonon-mediated interactions. As illustrative examples, we consider the antiferromagnetic phase in the three-dimensional model and the d-wave superconductor in two dimensions, analyzing the effect of the electron-phonon coupling, including its frequency dependence, on both instabilities.

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Emin Moghadas, Samuele Giuli, Massimo Capone, Alessandro Toschi. 2026-10-06. Dynamical vertex approximation for retarded interactions: Application to the Hubbard-Holstein model. https://arxiv.org/abs/2610.08512

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