Dynamical vertex approximation for retarded interactions: Application to the Hubbard-Holstein model
Abstract
We extend the dynamical vertex approximation (DΓA), in its most commonly used ladder-version, to systems with retarded electronic interactions. Such an extended scheme, which we name "dynamical-U DΓA", 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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BibTeX
@misc{moghadas2026dynamical,
title = {{Dynamical vertex approximation for retarded interactions: Application to the Hubbard-Holstein model}},
author = {Emin Moghadas and Samuele Giuli and Massimo Capone and Alessandro Toschi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08512},
eprint = {2610.08512},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08512},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Dynamical vertex approximation for retarded interactions: Application to the Hubbard-Holstein model
AU - Emin Moghadas
AU - Samuele Giuli
AU - Massimo Capone
AU - Alessandro Toschi
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.08512
UR - https://arxiv.org/abs/2610.08512
AB - We extend the dynamical vertex approximation (DΓA), in its most commonly used ladder-version, to systems with retarded electronic interactions. Such an extended scheme, which we name "dynamical-U DΓA", 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.
ER -