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update tolle and scott arxiv

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Antoine Marie 2023-04-23 15:19:45 +02:00
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48
Manuscript/SRGGW.bib
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@ -6,21 +6,6 @@
%% Saved with string encoding Unicode (UTF-8)
@article{Scott_2023,
author = {Scott,Charles Jeffrey Cargill and Backhouse,Oliver J and Booth,George Henry},
date-added = {2023-03-10 09:14:29 +0100},
date-modified = {2023-03-10 09:14:42 +0100},
doi = {10.1063/5.0143291},
journal = {J. Chem. Phys.},
number = {ja},
pages = {null},
title = {A 'moment-conserving' reformulation of {{GW}} theory},
volume = {0},
year = {0},
bdsk-url-1 = {https://doi.org/10.1063/5.0143291}}
@article{Biswas_2021,
author = {Biswas, T. and Singh, A.K.},
date-added = {2023-02-03 21:59:35 +0100},
@ -499,16 +484,7 @@
year = {2022},
bdsk-url-1 = {https://doi.org/10.1140/epja/s10050-022-00694-x}}
@misc{Tolle_2022,
archiveprefix = {arXiv},
author = {T{\"o}lle, Johannes and Chan, Garnet Kin-Lic},
doi = {10.48550/arXiv.2212.08982},
eprint = {2212.08982},
eprinttype = {arxiv},
number = {arXiv:2212.08982},
title = {Exact Relationships between the {{GW}} Approximation and Equation-of-Motion Coupled-Cluster Theories through the Quasi-Boson Formalism},
year = {2022},
bdsk-url-1 = {https://doi.org/10.48550/arXiv.2212.08982}}
@inbook{Bartlett_1986,
abstract = {A diagrammatic derivation of the coupled-cluster (CC) linear response equations for gradients is presented. MBPT approximations emerge as low-order iterations of the CC equations. In CC theory a knowledge of the change in cluster amplitudes with displacement is required, which would not be necessary if the coefficients were variationally optimum, as in the CI approach. However, it is shown that the CC linear response equations can be put in a form where there is no more difficulty in evaluating CC gradients than in the variational CI procedure. This offers a powerful approach for identifying critical points on energy surfaces and in evaluating other properties than the energy.},
@ -602,6 +578,28 @@
year = {2018},
bdsk-url-1 = {https://doi.org/10.1063/1.5039496}}
@article{Tolle_2023,
author = {T\"olle, Johannes and Chan, Garnet Kin-Lic},
doi = {10.1063/5.0139716},
journal = {J. Chem. Phys.},
number = {12},
pages = {124123},
title = {Exact relationships between the $GW$ approximation and equation-of-motion coupled-cluster theories through the quasi-boson formalism },
volume = {158},
year = {2023}}
@article{Scott_2023,
author = {Scott, Charles J. C. and Backhouse, Oliver J. and Booth, George H.},
doi = {10.1063/5.0143291},
journal = {J. Chem. Phys.},
volume = {158},
number = {12},
title = "{A “moment-conserving” reformulation of GW theory}",
year = {2023},
pages = {124102}
}
@article{McKeon_2022,
author = {McKeon,Caroline A. and Hamed,Samia M. and Bruneval,Fabien and Neaton,Jeffrey B.},
date-added = {2022-10-11 21:50:49 +0200},

4
Manuscript/SRGGW.tex
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@ -342,7 +342,7 @@ Then, as performed in Sec.~\ref{sec:srggw}, one can collect order by order the t
Here, we combine the concepts of the two previous subsections and apply the SRG method to the $GW$ formalism.
However, to do so, one must identify the coupling terms in Eq.~\eqref{eq:quasipart_eq}, which is not straightforward.
A way around this problem is to transform Eq.~\eqref{eq:quasipart_eq} to an equivalent upfolded form which elegantly highlights the coupling terms.
Indeed, the $GW$ quasiparticle equation is equivalent to the diagonalization of the following matrix \cite{Bintrim_2021,Tolle_2022}
Indeed, the $GW$ quasiparticle equation is equivalent to the diagonalization of the following matrix \cite{Bintrim_2021,Tolle_2023}
\begin{equation}
\label{eq:GWlin}
\begin{pmatrix}
@ -392,7 +392,7 @@ which can be further developed to recover exactly Eq.~\eqref{eq:GW_selfenergy}.
Equations \eqref{eq:GWlin} and \eqref{eq:quasipart_eq} yield exactly the same quasiparticle and satellite energies but one is linear and the other is not.
The price to pay for this linearity is that the size of the matrix in the former is $\order{K^3}$ while it is only $\order{K}$ in the latter.
We refer to Ref.~\onlinecite{Bintrim_2021} for a detailed discussion of the up/downfolding processes of the $GW$ equations (see also Refs.~\onlinecite{Tolle_2022,Scott_2023}).
We refer to Ref.~\onlinecite{Bintrim_2021} for a detailed discussion of the up/downfolding processes of the $GW$ equations (see also Refs.~\onlinecite{Tolle_2023,Scott_2023}).
As can be readily seen in Eq.~\eqref{eq:GWlin}, the blocks $\bW^\text{2h1p}$ and $\bW^\text{2p1h}$ are coupling the 1h and 1p configuration to the 2h1p and 2p1h configurations.
Therefore, it is natural to define, within the SRG formalism, the diagonal and off-diagonal parts of the $GW$ effective Hamiltonian as