Corrections post meeting

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Antoine Marie 2023-03-28 13:34:50 +02:00
parent 54e5828393
commit 9d1a5eca1e
3 changed files with 17 additions and 8 deletions

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@ -180,7 +180,7 @@ S. D. Głazek and K. G. Wilson, Phys. Rev. D 48, 5863 (1993)
\hfill\vline\hfill \hfill\vline\hfill
\begin{minipage}{0.49\linewidth} \begin{minipage}{0.49\linewidth}
\begin{tikzfigure} \begin{tikzfigure}
\includegraphics[width=1.1\textwidth]{SRGMatrix} \includegraphics[width=1.\textwidth]{SRGMatrix}
\end{tikzfigure} \end{tikzfigure}
\end{minipage} \end{minipage}
} }
@ -220,14 +220,21 @@ S. D. Głazek and K. G. Wilson, Phys. Rev. D 48, 5863 (1993)
\block{Functional form of the qs$GW$ and SRG-qs$GW$} \block{Functional form of the qs$GW$ and SRG-qs$GW$}
{ {
\begin{adjustbox}{valign=t}
\begin{minipage}[t]{0.25\linewidth}
\begin{tikzfigure}
\includegraphics[width=0.82\textwidth]{fig2a.pdf}
\end{tikzfigure}
\end{minipage}
\end{adjustbox}
\begin{minipage}[t]{0.5\linewidth} \begin{minipage}[t]{0.5\linewidth}
\begin{itemize} \begin{itemize}
\bigskip \bigskip
\item qs$GW$ self-energy: \item qs$GW$ self-energy:
\bigskip \bigskip
\begin{equation*} \begin{equation*}
\boxed{\boldsymbol{\Sigma}^{\text{qs}GW}_{pq}(\eta) = \boldsymbol{\Sigma}^{\text{qs}GW}_{pq}(\eta) =
\sum_{r\nu} \frac{1}{2}\qty(\frac{\Delta_{pr}^{\nu}}{(\Delta_{pr}^{\nu})^2 + \eta^2 } + \frac{\Delta_{qr}^{\nu}}{(\Delta_{qr}^{\nu})^2 + \eta^2}) W_{pr}^{\nu} W_{qr}^{\nu}} \sum_{r\nu} \frac{1}{2}\qty(\frac{\Delta_{pr}^{\nu}}{(\Delta_{pr}^{\nu})^2 + \eta^2 } + \frac{\Delta_{qr}^{\nu}}{(\Delta_{qr}^{\nu})^2 + \eta^2}) W_{pr}^{\nu} W_{qr}^{\nu}
\end{equation*} \end{equation*}
\bigskip \bigskip
{\small S. V. Faleev, M. van Schilfgaarde, and T. Kotani, Phys. Rev. Lett. 93, 126406 (2004)} {\small S. V. Faleev, M. van Schilfgaarde, and T. Kotani, Phys. Rev. Lett. 93, 126406 (2004)}
@ -235,16 +242,18 @@ S. D. Głazek and K. G. Wilson, Phys. Rev. D 48, 5863 (1993)
\item SRG-qs$GW$ self-energy: \item SRG-qs$GW$ self-energy:
\bigskip \bigskip
\begin{equation*} \begin{equation*}
\boxed{\boldsymbol{\Sigma}^{\text{SRG-qs}GW}_{pq}(s) = \boldsymbol{\Sigma}^{\text{SRG-qs}GW}_{pq}(s) =
\sum_{r\nu} \frac{\Delta_{pr}^{\nu} + \Delta_{qr}^{\nu}}{(\Delta_{pr}^{\nu})^2 + (\Delta_{qr}^{\nu})^2 } W_{pr}^{\nu} W_{qr}^{\nu} \qty[1 - e^{-((\Delta_{pr}^{\nu})^2+(\Delta_{qr}^{\nu})^2) s} ]} \sum_{r\nu} \frac{\Delta_{pr}^{\nu} + \Delta_{qr}^{\nu}}{(\Delta_{pr}^{\nu})^2 + (\Delta_{qr}^{\nu})^2 } W_{pr}^{\nu} W_{qr}^{\nu} \qty[1 - e^{-((\Delta_{pr}^{\nu})^2+(\Delta_{qr}^{\nu})^2) s} ]
\end{equation*} \end{equation*}
\bigskip
{\small A. Marie and P.-F. Loos, arXiv:2303.05984 (2023)}
\end{itemize} \end{itemize}
\bigskip \bigskip
\end{minipage} \end{minipage}
\begin{adjustbox}{valign=t} \begin{adjustbox}{valign=t}
\begin{minipage}[t]{0.5\linewidth} \begin{minipage}[t]{0.25\linewidth}
\begin{tikzfigure} \begin{tikzfigure}
\includegraphics[width=0.82\textwidth]{fig2.pdf} \includegraphics[width=0.82\textwidth]{fig2b.pdf}
\end{tikzfigure} \end{tikzfigure}
\end{minipage} \end{minipage}
\end{adjustbox} \end{adjustbox}
@ -291,6 +300,6 @@ S. D. Głazek and K. G. Wilson, Phys. Rev. D 48, 5863 (1993)
This project has received funding from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (Grant agreement No. 863481).} This project has received funding from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (Grant agreement No. 863481).}
\end{columns} \end{columns}
\node [above right,outer sep=0pt,minimum width=\paperwidth,align=left,draw,fill=footer] at (bottomleft) {\Large \textcolor{white}{\textbf{amarie@irsamc.ups-tlse.fr \hspace{50cm} arXiv:2303.05984}} }; \node [above right,outer sep=0pt,minimum width=\paperwidth,align=left,draw,fill=footer] at (bottomleft) {\Large \textcolor{white}{\textbf{amarie@irsamc.ups-tlse.fr} }};
\end{document} \end{document}