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D. Głazek and K. G. Wilson, Phys. Rev. D 48, 5863 (1993) \hfill\vline\hfill \begin{minipage}{0.49\linewidth} \begin{tikzfigure} - \includegraphics[width=1.1\textwidth]{SRGMatrix} + \includegraphics[width=1.\textwidth]{SRGMatrix} \end{tikzfigure} \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$GW$} { + \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{itemize} \bigskip \item qs$GW$ self-energy: \bigskip \begin{equation*} - \boxed{\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}} + \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} \end{equation*} \bigskip {\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: \bigskip \begin{equation*} - \boxed{\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} ]} + \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} ] \end{equation*} + \bigskip + {\small A. Marie and P.-F. Loos, arXiv:2303.05984 (2023)} \end{itemize} \bigskip \end{minipage} \begin{adjustbox}{valign=t} - \begin{minipage}[t]{0.5\linewidth} + \begin{minipage}[t]{0.25\linewidth} \begin{tikzfigure} - \includegraphics[width=0.82\textwidth]{fig2.pdf} + \includegraphics[width=0.82\textwidth]{fig2b.pdf} \end{tikzfigure} \end{minipage} \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 Union’s Horizon 2020 research and innovation programme (Grant agreement No. 863481).} \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}