diff --git a/Poster/ERC.png b/Poster/ERC.png index 78ac375..7115964 100644 Binary files a/Poster/ERC.png and b/Poster/ERC.png differ diff --git a/Poster/fig3.pdf b/Poster/fig3.pdf index c9d6fac..3b19cb8 100644 Binary files a/Poster/fig3.pdf and b/Poster/fig3.pdf differ diff --git a/Poster/fig4.pdf b/Poster/fig4.pdf index 9e5b869..b483407 100644 Binary files a/Poster/fig4.pdf and b/Poster/fig4.pdf differ diff --git a/Poster/main.tex b/Poster/main.tex index 05be94f..461b08f 100644 --- a/Poster/main.tex +++ b/Poster/main.tex @@ -17,6 +17,39 @@ \date{\today} \institute{Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, France} +\definecolor{darkgreen}{RGB}{0, 180, 0} +\definecolor{fooblue}{RGB}{0,153,255} +\definecolor{fooyellow}{RGB}{234,180,0} +\definecolor{lavender}{rgb}{0.71, 0.49, 0.86} +\definecolor{inchworm}{rgb}{0.7, 0.93, 0.36} +\newcommand{\violet}[1]{\textcolor{violet}{#1}} +\newcommand{\orange}[1]{\textcolor{orange}{#1}} +\newcommand{\purple}[1]{\textcolor{purple}{#1}} +\newcommand{\blue}[1]{\textcolor{blue}{#1}} +\newcommand{\green}[1]{\textcolor{darkgreen}{#1}} +\newcommand{\yellow}[1]{\textcolor{fooyellow}{#1}} +\newcommand{\red}[1]{\textcolor{red}{#1}} +\newcommand{\cyan}[1]{\textcolor{cyan}{#1}} +\newcommand{\magenta}[1]{\textcolor{magenta}{#1}} +\newcommand{\highlight}[1]{\textcolor{fooblue}{#1}} +\newcommand{\pub}[1]{\textcolor{purple}{#1}} + +\newcommand{\bSig}{\boldsymbol{\Sigma}} +\newcommand{\bSigC}{\boldsymbol{\Sigma}^{\text{c}}} +\newcommand{\be}{\boldsymbol{\epsilon}} +\newcommand{\bOm}{\boldsymbol{\Omega}} +\newcommand{\bEta}[1]{\boldsymbol{\eta}^{(#1)}(s)} + +\newcommand{\ii}{\mathrm{i}} +\newcommand{\GW}{GW} +\newcommand{\GF}{\text{GF(2)}} +\newcommand{\GT}{GT} +\newcommand{\evGW}{\text{ev}GW} +\newcommand{\qsGW}{\text{qs}GW} +\newcommand{\SRGGW}{\text{SRG-}GW} +\newcommand{\SRGqsGW}{\text{SRG-qs}GW} +\newcommand{\GOWO}{G_0W_0} + \makeatletter \newcommand\insertlogoi[2][]{\def\@insertlogoi{\includegraphics[#1]{#2}}} \newcommand\insertlogoii[2][]{\def\@insertlogoii{\includegraphics[#1]{#2}}} @@ -92,10 +125,31 @@ \begin{columns} \column{0.5} - \block{GW}{\blindtext} + \block{Dynamic $GW$} + { + \begin{minipage}{0.4\linewidth} + \begin{tikzfigure} + \includegraphics[width=0.8\textwidth]{square} + \end{tikzfigure} + \end{minipage} + \begin{minipage}{0.6\linewidth} + \begin{equation*} + \qty[ \underbrace{\blue{\boldsymbol{F}}}_{\text{\blue{Fock matrix}}} + \underbrace{\violet{\boldsymbol{\Sigma}^{\GW}} (\omega = \epsilon^{GW}_{p})}_{\text{\violet{dynamic self-energy}}} ] \psi_{p}^{GW} + = \epsilon^{GW}_{p} \psi_{p}^{GW} + \end{equation*} + \vspace{1cm} + \begin{equation*} + \begin{split} + \violet{\Sigma_{pq}^{GW}}(\omega) + &= \sum_{i\nu} \frac{\red{W_{pi}^{\nu}} \red{W_{qi}^{\nu}}}{\omega - \epsilon^{GW}_{i} + \orange{\Omega_{\nu}} - \ii \eta} \\ + &+ \sum_{a\nu} \frac{\red{W_{pa}^{\nu}} \red{W_{qa}^{\nu}}}{\omega - \epsilon^{GW}_{a} - \orange{\Omega_{\nu}} + \ii \eta} + \end{split} + \end{equation*} + \end{minipage} + } \column{0.5} \block{SRG}{ - \begin{minipage}[t]{0.48\linewidth} + \begin{minipage}{0.49\linewidth} The pillar of the SRG formalism is the flow equation \begin{equation} \label{eq:flowEquation} @@ -115,61 +169,100 @@ \end{equation} \end{minipage} \hfill\vline\hfill - \begin{minipage}[t]{0.48\linewidth} - BLABLABLA + \begin{minipage}{0.49\linewidth} + \begin{tikzfigure} + \includegraphics[width=0.9\textwidth]{SRGMatrix} + \end{tikzfigure} \end{minipage} } \end{columns} -\block{SRG-GW} - { - \begin{minipage}{0.7\linewidth} - \blindtext - \end{minipage} - \begin{minipage}{0.3\linewidth} - \begin{tikzfigure} - \includegraphics[width=0.85\textwidth]{fig1.pdf} - \end{tikzfigure} - \end{minipage} - } - - \block{Functional form of the qs$GW$ and SRG-qs$GW$}{ - \begin{minipage}[t]{0.25\linewidth} - BLABLABLA - \end{minipage} - \begin{adjustbox}{valign=t} - \begin{minipage}[t]{0.5\linewidth} - \begin{tikzfigure} - \includegraphics[width=0.8\textwidth]{fig2.pdf} - \end{tikzfigure} - \end{minipage} - \end{adjustbox} - \begin{minipage}[t]{0.25\linewidth} - BLABLABLA - \end{minipage} - } - \begin{columns} - \column{0.5} - \block{Something else}{ - \begin{tikzfigure} - \includegraphics[height=15cm]{fig3.pdf} - \end{tikzfigure}} - \column{0.5} - \block{$GW$50 statistics}{ - \begin{tikzfigure} - \includegraphics[height=15cm]{fig6.pdf} - \end{tikzfigure}} - + \column{0.35} + \block{Static $GW$} + { + \begin{tikzfigure} + \includegraphics[width=0.29\textwidth]{upfolding.pdf} + \end{tikzfigure}} + \column{0.65} + \block{SRG-$GW$} + { + \begin{minipage}{0.575\linewidth} + \begin{equation*} + \begin{split} + &\blue{\widetilde{\boldsymbol{F}}_{pq}}(s) = \delta_{pq} \blue{\epsilon^{\text{HF}}_{p}} + \sum_{r\nu} \frac{\Delta_{pr}^{\nu} + \Delta_{qr}^{\nu}}{(\Delta_{pr}^{\nu})^2 + (\Delta_{qr}^{\nu})^2 } \red{W_{pr}^{\nu}} \red{W_{qr}^{\nu}} \qty[1 - e^{-((\Delta_{pr}^{\nu})^2+(\Delta_{qr}^{\nu})^2) s} ] \\ + &\qq{with} \Delta_{pr}^{\nu} = \epsilon^{GW}_{p} - \epsilon^{GW}_{r} \pm \Omega_\nu \\ + \\ + &\violet{\widetilde{\Sigma}_{pq}^{\SRGGW}}(\omega;s) = \\ + &\sum_{i\nu} \frac{\red{W_{pi}^{\nu}} \red{W_{qi}^{\nu}}e^{-((\Delta_{pi}^{\nu})^2+(\Delta_{qi}^{\nu})^2) s}}{\omega - \epsilon^{GW}_{i} + \Omega_{\nu}} + \sum_{a\nu} \frac{\red{W_{pa}^{\nu}} \red{W_{qa}^{\nu}}e^{-((\Delta_{pa}^{\nu})^2+(\Delta_{qa}^{\nu})^2) s}}{\omega - \epsilon^{GW}_{a} - \Omega_{\nu}} + \end{split} + \end{equation*} + \end{minipage} + \begin{minipage}{0.425\linewidth} + \begin{tikzfigure} + \includegraphics[width=\textwidth]{fig1.pdf} + \end{tikzfigure} + \end{minipage} + } + \end{columns} +\block{Functional form of the qs$GW$ and SRG-qs$GW$} +{ + \begin{minipage}[t]{0.275\linewidth} + \vspace{2.5cm} + \begin{equation*} + \begin{split} + &\boldsymbol{\Sigma}^{\text{qs}GW}_{pq}(\eta) = \delta_{pq} \epsilon^{\text{HF}}_{p} + \\ + \\ + &\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{split} + \end{equation*} + \end{minipage} + \begin{adjustbox}{valign=t} + \begin{minipage}[t]{0.45\linewidth} + \begin{tikzfigure} + \includegraphics[width=0.8\textwidth]{fig2.pdf} + \end{tikzfigure} + \end{minipage} + \end{adjustbox} + \begin{minipage}[t]{0.275\linewidth} + \vspace{2.5cm} + \begin{equation*} + \begin{split} + &\boldsymbol{\Sigma}^{\text{SRG-qs}GW}_{pq}(s) = \delta_{pq} \epsilon^{\text{HF}}_{p} + \\ + \\ + &\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{split} + \end{equation*} + \end{minipage} +} +\begin{columns} + \column{0.33} + \block{IP flow parameter dependence}{ + \begin{tikzfigure} + \includegraphics[height=14cm]{fig3.pdf} + \end{tikzfigure}} + \column{0.33} + \block{EA flow parameter dependence}{ + \begin{tikzfigure} + \includegraphics[height=14cm]{fig4.pdf} + \end{tikzfigure}} + \column{0.33} + \block{MAE flow parameter dependence}{ + \begin{tikzfigure} + \includegraphics[height=14cm]{fig6.pdf} + \end{tikzfigure}} + + \end{columns} + \begin{columns} \column{0.85} \block{$GW$50 statistics}{ \begin{tikzfigure} - \includegraphics[height=15cm]{fig5.pdf} + \includegraphics[height=14cm]{fig5.pdf} \end{tikzfigure}} \column{0.15} \block{Funding}{