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modifs in manuscript

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Pierre-Francois Loos 2023-05-11 19:52:47 +02:00
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Manuscript/SRGGW.tex
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@ -207,7 +207,7 @@ with
\end{subequations} \end{subequations}
and where and where
\begin{equation} \begin{equation}
\braket{pq}{rs} = \iint \frac{\textcolor{red}{\SO{p}^*(\bx_1) \SO{q}^*(\bx_2)}\SO{r}(\bx_1) \SO{s}(\bx_2) }{\abs{\br_1 - \br_2}} d\bx_1 d\bx_2 \braket{pq}{rs} = \iint \frac{\SO{p}(\bx_1) \SO{q}(\bx_2)\SO{r}(\bx_1) \SO{s}(\bx_2) }{\abs{\br_1 - \br_2}} d\bx_1 d\bx_2
\end{equation} \end{equation}
are bare two-electron integrals in the spin-orbital basis. are bare two-electron integrals in the spin-orbital basis.
@ -633,11 +633,13 @@ Performing a bijective transformation of the form,
e^{- \Delta s} &= 1-e^{-\Delta t}, e^{- \Delta s} &= 1-e^{-\Delta t},
\end{align} \end{align}
on the renormalized quasiparticle equation \eqref{eq:GW_renorm} reverses the situation and makes it possible to choose $t$ such that there is no intruder states in the dynamic part, hence removing discontinuities. on the renormalized quasiparticle equation \eqref{eq:GW_renorm} reverses the situation and makes it possible to choose $t$ such that there is no intruder states in the dynamic part, hence removing discontinuities.
\textcolor{red}{The intruder-state free dynamic part makes it possible to define a SRG-$G_0W_0$ and SRG-ev$GW$.
The main manuscript focus on SRG-qs$GW$ but the performance of SRG-$G_0W_0$ and SRG-ev$GW$ are discussed in the {\SupInf} for the sake of completeness.}
Note that, after this transformation, the form of the regularizer is actually closely related to the SRG-inspired regularizer introduced by Monino and Loos in Ref.~\onlinecite{Monino_2022}. Note that, after this transformation, the form of the regularizer is actually closely related to the SRG-inspired regularizer introduced by Monino and Loos in Ref.~\onlinecite{Monino_2022}.
\textcolor{red}{The intruder-state-free dynamic part of the self-energy makes it possible to define SRG-$G_0W_0$ and SRG-ev$GW$ schemes.
Although the manuscript focuses on SRG-qs$GW$, the performance of SRG-$G_0W_0$ and SRG-ev$GW$ are discussed in the {\SupInf} for the sake of completeness.
In a nutshell, the SRG regularization improves the overall convergence properties of SRG-ev$GW$ without altering its performance.
Likewise, the statistical indicators for $G_0W_0$ and SRG-$G_0W_0$ are extremely close.}
%=================================================================% %=================================================================%
\section{Computational details} \section{Computational details}
\label{sec:comp_det} \label{sec:comp_det}