GW reduced density matrix from iterated linearized Dyson equation
Abstract
Iterating the Dyson equation with the static part of the self-energy leads to a concise and possibly improved expression of the one-body reduced density matrix from any self-energy approximation. Here we apply the procedure to Hedin's GW approximation. The non-iterated GW based density matrix was already known to yield accurate density matrices for molecular systems. We show that the Dyson-equation-based procedure is equivalent to the so-called variational Z-vector approach applied to the Random-Phase approximation energy functional, but only in the case of a Hartree-Fock mean-field starting point. When a generalized Kohn-Sham scheme is employed instead, the two approaches differ. By comparing the density matrix for a benchmark set of 34 small molecules to coupled-cluster reference values, we conclude that the iterated Dyson equation indeed produces improved density matrices for molecular systems. Interestingly, we observe that the excitation rank of the reference coupled-cluster matters much and that the inclusion of triple excitations (CCSDT) quantitatively changes the conclusions of the benchmark as compared to single and double excitations coupled-cluster (CCSD).
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BibTeX
@misc{bruneval2026reduced,
title = {{$GW$ reduced density matrix from iterated linearized Dyson equation}},
author = {Fabien Bruneval and Erik Verzijl and Arno Förster and Mauricio Rodriguez-Mayorga},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.15695},
eprint = {2607.15695},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.15695},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - GW reduced density matrix from iterated linearized Dyson equation
AU - Fabien Bruneval
AU - Erik Verzijl
AU - Arno Förster
AU - Mauricio Rodriguez-Mayorga
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2607.15695
UR - https://arxiv.org/abs/2607.15695
AB - Iterating the Dyson equation with the static part of the self-energy leads to a concise and possibly improved expression of the one-body reduced density matrix from any self-energy approximation. Here we apply the procedure to Hedin's GW approximation. The non-iterated GW based density matrix was already known to yield accurate density matrices for molecular systems. We show that the Dyson-equation-based procedure is equivalent to the so-called variational Z-vector approach applied to the Random-Phase approximation energy functional, but only in the case of a Hartree-Fock mean-field starting point. When a generalized Kohn-Sham scheme is employed instead, the two approaches differ. By comparing the density matrix for a benchmark set of 34 small molecules to coupled-cluster reference values, we conclude that the iterated Dyson equation indeed produces improved density matrices for molecular systems. Interestingly, we observe that the excitation rank of the reference coupled-cluster matters much and that the inclusion of triple excitations (CCSDT) quantitatively changes the conclusions of the benchmark as compared to single and double excitations coupled-cluster (CCSD).
ER -