Bogoliubov self-consistent GW and second-order Green's function methods for attractive fermionic interactions
Abstract
Describing fermionic systems with attractive interactions, such as superconductors and atomic nuclei, beyond the mean-field level remains a central challenge. In this work, we investigate the performance of Bogoliubov fully self-consistent GW (Bog.~scGW) and second-order Green's function (Bog.~scGF2) methods, implemented within a unified imaginary-time and imaginary-frequency framework. Using the attractive Hubbard model as a benchmark against full configuration interaction (FCI), we find that Bog. scGF2 provides a more accurate description than Bog.~scGW. In particular, Bog.~scGW systematically overestimates the correlation energy, with errors increasing rapidly as the attractive interaction strength grows. These results highlight the importance of exchange contributions in strongly correlated fermionic systems, even when exchange effects are included only at low order in perturbation theory.
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BibTeX
@misc{rodriguezmayorga2026bogoliubov,
title = {{Bogoliubov self-consistent $GW$ and second-order Green's function methods for attractive fermionic interactions}},
author = {Mauricio Rodríguez-Mayorga and Johannes Tölle and Pierre-François Loos},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03357},
eprint = {2610.03357},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03357},
}
RIS
TY - UNPB
TI - Bogoliubov self-consistent GW and second-order Green's function methods for attractive fermionic interactions
AU - Mauricio Rodr{í}guez-Mayorga
AU - Johannes Tölle
AU - Pierre-François Loos
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03357
UR - https://arxiv.org/abs/2610.03357
AB - Describing fermionic systems with attractive interactions, such as superconductors and atomic nuclei, beyond the mean-field level remains a central challenge. In this work, we investigate the performance of Bogoliubov fully self-consistent GW (Bog.~scGW) and second-order Green's function (Bog.~scGF2) methods, implemented within a unified imaginary-time and imaginary-frequency framework. Using the attractive Hubbard model as a benchmark against full configuration interaction (FCI), we find that Bog. scGF2 provides a more accurate description than Bog.~scGW. In particular, Bog.~scGW systematically overestimates the correlation energy, with errors increasing rapidly as the attractive interaction strength grows. These results highlight the importance of exchange contributions in strongly correlated fermionic systems, even when exchange effects are included only at low order in perturbation theory.
ER -