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Pierre-Francois Loos 2023-03-09 21:57:53 +01:00
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Manuscript/SRGGW.tex
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@ -85,7 +85,7 @@ The SRG formalism enables us to derive, from first principles, the expression of
The resulting SRG-based regularized self-energy significantly accelerates the convergence of qs$GW$ calculations, slightly improves the overall accuracy, and is straightforward to implement in existing code. The resulting SRG-based regularized self-energy significantly accelerates the convergence of qs$GW$ calculations, slightly improves the overall accuracy, and is straightforward to implement in existing code.
\bigskip \bigskip
\begin{center} \begin{center}
\boxed{\includegraphics[width=0.5\linewidth]{flow}} \boxed{\includegraphics[width=0.5\linewidth]{TOC}}
\end{center} \end{center}
\bigskip \bigskip
\end{abstract} \end{abstract}
@ -554,7 +554,7 @@ which can be solved by simple integration along with the initial condition $\bF^
%%% FIG 1 %%% %%% FIG 1 %%%
\begin{figure} \begin{figure}
\centering \centering
\includegraphics[width=\linewidth]{flow} \includegraphics[width=\linewidth]{fig1}
\caption{ \caption{
Schematic evolution of the quasiparticle equation as a function of the flow parameter $s$ in the case of the dynamic SRG-$GW$ flow (magenta) and the static SRG-qs$GW$ flow (cyan). Schematic evolution of the quasiparticle equation as a function of the flow parameter $s$ in the case of the dynamic SRG-$GW$ flow (magenta) and the static SRG-qs$GW$ flow (cyan).
\label{fig:flow}} \label{fig:flow}}
@ -718,7 +718,7 @@ The denominators of the 2p1h term are positive while the denominators associated
As $s$ increases, the first states that decouple from the HOMO are the 2p1h configurations because their energy difference with respect to the HOMO is larger than the ones associated with the 2h1p block. As $s$ increases, the first states that decouple from the HOMO are the 2p1h configurations because their energy difference with respect to the HOMO is larger than the ones associated with the 2h1p block.
Therefore, for small $s$, only the last term of Eq.~\eqref{eq:2nd_order_IP} is partially included, resulting in a positive correction to the IP. Therefore, for small $s$, only the last term of Eq.~\eqref{eq:2nd_order_IP} is partially included, resulting in a positive correction to the IP.
As soon as $s$ is large enough to decouple the 2h1p block, the IP starts decreasing and eventually goes below the $s=0$ initial value as observed in Fig.~\ref{fig:fig3}. As soon as $s$ is large enough to decouple the 2h1p block, the IP starts decreasing and eventually goes below the initial value at $s=0$, as observed in Fig.~\ref{fig:fig3}.
%\ANT{I don't know if we should remove this paragraph and the TDA curves in Fig 3 and 4 or not...} %\ANT{I don't know if we should remove this paragraph and the TDA curves in Fig 3 and 4 or not...}
%In addition, the qs$GW$ and SRG-qs$GW$ methods based on a TDA screening (dubbed qs$GW^\TDA$ and SRG-qs$GW^\TDA$) are also considered in Fig.~\ref{fig:fig3}. %In addition, the qs$GW$ and SRG-qs$GW$ methods based on a TDA screening (dubbed qs$GW^\TDA$ and SRG-qs$GW^\TDA$) are also considered in Fig.~\ref{fig:fig3}.
@ -882,7 +882,7 @@ These convergence problems are much more dramatic than for SRG-qs$GW$ because th
For example, out of the 37 molecules that could be converged for $\eta=\num{e-2}$, the variation of the IP with respect to $\eta=\num{5e-2}$ can go up to \SI{0.1}{\eV}. For example, out of the 37 molecules that could be converged for $\eta=\num{e-2}$, the variation of the IP with respect to $\eta=\num{5e-2}$ can go up to \SI{0.1}{\eV}.
This difference in behavior is due to the energy (in)dependence of the regularizers. This difference in behavior is due to the energy (in)dependence of the regularizers.
Indeed, the SRG regularizer first includes the terms that are \ant{contributing to} the energy and finally adds the intruder states. Indeed, the SRG regularizer first includes the terms that are \titou{contributing to} the energy and finally adds the intruder states.
On the other hand, the imaginary shift regularizer acts equivalently on all terms. On the other hand, the imaginary shift regularizer acts equivalently on all terms.
%%% FIG 7 %%% %%% FIG 7 %%%

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Manuscript/flow.pdf → Manuscript/TOC.pdf
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