diff --git a/Sanibel_2023/Sanibel23-Loos.tex b/Sanibel_2023/Sanibel23-Loos.tex new file mode 100644 index 0000000..0991e04 --- /dev/null +++ b/Sanibel_2023/Sanibel23-Loos.tex @@ -0,0 +1,707 @@ +\documentclass[9pt,aspectratio=169]{beamer} +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{hyperref} +\usepackage{mathtools,amsmath,amssymb,amsfonts,graphicx,xcolor,bm,microtype,wasysym,hyperref,tabularx,amscd,mhchem,physics} +\usepackage{emoji} +\usepackage[normalem]{ulem} +\newcommand\hcancel[2][black]{\setbox0=\hbox{$#2$}% +\rlap{\raisebox{.45\ht0}{\textcolor{#1}{\rule{\wd0}{1pt}}}}#2} +\urlstyle{same} + +\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{lavender}{#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{\mc}{\multicolumn} +\newcommand{\fnm}{\footnotemark} +\newcommand{\fnt}{\footnotetext} +\newcommand{\tabc}[1]{\multicolumn{1}{c}{#1}} +\newcommand{\QP}{\textsc{quantum package}} +\newcommand{\T}[1]{#1^{\intercal}} + +% coordinates +\newcommand{\br}{\boldsymbol{r}} +\newcommand{\bx}{\boldsymbol{x}} + +% methods +\newcommand{\NO}[1]{\{#1\}} +\newcommand{\GW}{GW} +\newcommand{\SRGGW}{\text{SRG-$GW$}} +\newcommand{\SRGqsGW}{\text{SRG-qs$GW$}} +\newcommand{\qs}{\text{qs}} +\newcommand{\qsGW}{\text{qs}GW} +\newcommand{\KS}{KS} +\newcommand{\GOWO}{G_0W_0} +\newcommand{\dRPA}{\text{dRPA}} +\newcommand{\RPAx}{\text{RPAx}} +\newcommand{\BSE}{\text{BSE}} +\newcommand{\CC}{\text{CC}} + +% +\newcommand{\Ne}{N} +\newcommand{\Norb}{K} +\newcommand{\Nocc}{O} +\newcommand{\Nvir}{V} + +% operators +\newcommand{\hH}{\Hat{H}} +\newcommand{\hP}{\Hat{P}} +\newcommand{\hQ}{\Hat{Q}} +\newcommand{\hU}{\Hat{U}} +\newcommand{\hI}{\Hat{I}} +\newcommand{\heta}{\Hat{\eta}} +\newcommand{\sH}{\Bar{H}} +\newcommand{\hHN}{\Hat{H}_{\text{N}}} +\newcommand{\hFN}{\Hat{F}_{\text{N}}} +\newcommand{\hVN}{\Hat{V}_{\text{N}}} +\newcommand{\hh}{\Hat{h}} +\newcommand{\hf}{\Hat{f}} +\newcommand{\bHN}{\Bar{H}_{\text{N}}} +\newcommand{\tHN}{\Tilde{H}_{\text{N}}} +\newcommand{\hT}{\Hat{T}} +\newcommand{\hS}{\Hat{S}} +\newcommand{\cre}[1]{\Hat{a}_{#1}^{\dag}} +\newcommand{\ani}[1]{\Hat{a}_{#1}} +\newcommand{\ca}[2]{\Hat{a}^{#1}_{#2}} + +\newcommand{\cF}{\mathcal{F}} +\newcommand{\cW}{\mathcal{W}} + +% energies +\newcommand{\Enuc}{E^\text{nuc}} +\newcommand{\Ec}{E_\text{c}} +\newcommand{\EHF}{E_\text{HF}} +\newcommand{\ECC}{E_\text{CC}} + +% orbital energies +\newcommand{\e}[2]{\epsilon_{#1}^{#2}} +\newcommand{\eHF}[1]{\epsilon_{#1}^\text{HF}} +\newcommand{\eKS}[1]{\epsilon_{#1}^\text{KS}} +\newcommand{\eGW}[1]{\epsilon_{#1}^{GW}} +\newcommand{\Om}{\Omega} +\newcommand{\eHOMO}[1]{\epsilon_\text{HOMO}^{#1}} +\newcommand{\eLUMO}[1]{\epsilon_\text{LUMO}^{#1}} + +% Matrix elements +\newcommand{\MO}[2]{\phi_{#1}^{#2}} +\newcommand{\SO}[2]{\psi_{#1}^{#2}} +\newcommand{\ERI}[2]{\braket{#1}{#2}} +\newcommand{\sERI}[2]{(#1|#2)} +\newcommand{\dbERI}[2]{\mel{#1}{}{#2}} +\newcommand{\Sig}{\Sigma} + +% Matrices +\newcommand{\bO}{\boldsymbol{0}} +\newcommand{\bH}{\boldsymbol{H}} +\newcommand{\bI}{\boldsymbol{1}} +\newcommand{\bpsi}{\boldsymbol{\psi}} +\newcommand{\bPsi}{\boldsymbol{\Psi}} +\newcommand{\bSig}{\boldsymbol{\Sigma}} +\newcommand{\bbH}{\Bar{\Bar{H}}} +\newcommand{\bOm}{\boldsymbol{\Omega}} +\newcommand{\bom}{\boldsymbol{\omega}} +\newcommand{\bA}{\boldsymbol{A}} +\newcommand{\bB}{\boldsymbol{B}} +\newcommand{\bC}{\boldsymbol{C}} +\newcommand{\bc}{\boldsymbol{c}} +\newcommand{\bD}{\boldsymbol{D}} +\newcommand{\bF}{\boldsymbol{F}} +\newcommand{\bR}{\boldsymbol{R}} +\newcommand{\bT}{\boldsymbol{T}} +\newcommand{\bU}{\boldsymbol{U}} +\newcommand{\bV}{\boldsymbol{V}} +\newcommand{\bW}{\boldsymbol{W}} +\newcommand{\bX}{\boldsymbol{X}} +\newcommand{\bY}{\boldsymbol{Y}} +\newcommand{\bZ}{\boldsymbol{Z}} +\newcommand{\bP}{\boldsymbol{P}} +\newcommand{\bQ}{\boldsymbol{Q}} +\newcommand{\be}{\boldsymbol{\epsilon}} + +% orbitals, gaps, etc +\newcommand{\IP}{I} +\newcommand{\EA}{A} +\newcommand{\HOMO}{\text{HOMO}} +\newcommand{\LUMO}{\text{LUMO}} +\newcommand{\Eg}[1]{E_\text{g}^{#1}} +\newcommand{\EgFun}{\Eg^\text{fund}} +\newcommand{\EgOpt}{\Eg^\text{opt}} +\newcommand{\EB}{E_B} + +\newcommand{\ii}{\mathrm{i}} +\newcommand{\om}{\yellow{\omega}} +\newcommand{\la}{\lambda} + + +\institute{Laboratoire de Chimie et Physique Quantiques, IRSAMC, UPS/CNRS, Toulouse\\ +\url{https://lcpq.github.io/pterosor}} +\usetheme{pterosor} +\author{Antoine Marie \& Pierre-Fran\c{c}ois Loos} +\date{Feb 13th 2023} +\title{A similarity renormalization group (SRG) approach to $GW$} + +\begin{document} + +\maketitle + +%----------------------------------------------------- +\begin{frame}{A SRG Approach to Green's Function Methods} + \begin{columns} + \begin{column}{0.75\textwidth} + \centering + \begin{figure}%[H] + \includegraphics[width=0.8\textwidth]{fig/flow} + \end{figure} + \end{column} + \begin{column}{0.25\textwidth} + \centering + \small + \includegraphics[width=0.8\textwidth]{fig/AMarie} + \\ + Antoine Marie (PhD) + \end{column} + \end{columns} + \bigskip + See also our work on the connections between CC and Green's function methods + \\ + \pub{Quintero-Monsebaiz, Monino, Marie \& Loos, JCP 157 (2022) 231102} + \\ + \bigskip + $\hookrightarrow$ \pub{Scuseria et al. JCP 129 (2008) 231101} + \\ + $\hookrightarrow$ \pub{Berkelbach, JCP 149 (2018) 041103; Lange \& Berkelbach, JCTC 14 (2018) 4224} + \\ + $\hookrightarrow$ \pub{Tolle \& Chan, arXiv:2212.08982} + +\end{frame} +%----------------------------------------------------- + +%----------------------------------------------------- +\begin{frame}{The $GW$ Approximation} + \begin{itemize} + \item[\emoji{nerd-face}] The $GW$ approximation allows us to access \alert{charged} excitations (IPs \& EAs) + \\ + \pub{Hedin, Phys. Rev. 139 (1965) A796} + \bigskip + \item[\emoji{face-with-monocle}] It yields accurate \alert{fundamental gaps} at an affordable price for \alert{solids} and \alert{molecules} + \\ + \pub{Bruneval et al. Front. Chem. 9 (2021) 749779} + \bigskip + \item[\emoji{smiling-face-with-halo}] $GW$ corresponds to an elegant resummation of the direct ring diagrams + \bigskip + \item[\emoji{partying-face}] Hence, it is adequate for weak correlation or in the high-density regime + \\ + \pub{Gell-Mann \& Brueckner, Phys. Rev. 106 (1957) 364} + \bigskip + \item[\emoji{confused}] \alert{Self-consistent} $GW$ calculations can be tricky to converge due to \alert{intruder states} + \\ + \pub{Monino \& Loos JCP 156 (2022) 231101} + \bigskip + \item[\emoji{cry}] Going \alert{beyond} $GW$ is, let's say, difficult\ldots + \\ + \pub{Mejuto-Zaera \& Vlcek, PRB 106 (2022) 165129} + \end{itemize} +% \pub{Martin, Reining \& Ceperley, \textit{Interacting Electrons: Theory and Computational Approaches}} +\end{frame} +%----------------------------------------------------- + +%----------------------------------------------------- +\begin{frame}{Hedin's Pentagon} + \begin{columns} + \begin{column}{0.4\textwidth} + \centering + \includegraphics[width=0.8\linewidth]{fig/pentagon} + \\ + \pub{Hedin, Phys Rev 139 (1965) A796} + \end{column} + \begin{column}{0.6\textwidth} + \begin{block}{The wonderful equations of Hedin} + \begin{align*} + & \underbrace{\yellow{G}(12)}_{\text{Green's function}} = G_0(12) + \int G_0(13) \violet{\Sigma}(34) \yellow{G}(42) d(34) + \\ + & \underbrace{\Gamma(123)}_{\text{vertex}} = \delta(12) \delta(13) + + \int \fdv{\violet{\Sigma}(12)}{\yellow{G}(45)} \yellow{G}(46) \yellow{G}(75) \Gamma(673) d(4567) + \\ + & \underbrace{\orange{P}(12)}_{\text{polarizability}} = - i \int \yellow{G}(13) \Gamma(342) \yellow{G}(41) d(34) + \\ + & \underbrace{\red{W}(12)}_{\text{screening}} = v(12) + \int v(13) \orange{P}(34) \red{W}(42) d(34) + \\ + & \underbrace{\violet{\Sigma}(12)}_{\text{self-energy}} = i \int \yellow{G}(14) \red{W}(13) \Gamma(423) d(34) + \end{align*} + \end{block} + \end{column} + \end{columns} +\end{frame} +%----------------------------------------------------- + + +%----------------------------------------------------- +\begin{frame}{Hedin's \sout{Pentagon} Square} + \begin{columns} + \begin{column}{0.4\textwidth} + \centering + \includegraphics[width=0.8\linewidth]{fig/square} + \\ + \pub{Hedin, Phys Rev 139 (1965) A796} + \end{column} + \begin{column}{0.6\textwidth} + \begin{block}{The $GW$ approximation} + \begin{align*} + & \underbrace{\yellow{G}(12)}_{\text{Green's function}} = G_0(12) + \int G_0(13) \violet{\Sigma}(34) \yellow{G}(42) d(34) + \\ + & \underbrace{\Gamma(123)}_{\text{vertex}} = \delta(12) \delta(13) + + \hcancel[red]{\int \fdv{\violet{\Sigma}(12)}{\yellow{G}(45)} \yellow{G}(46) \yellow{G}(75) \Gamma(673) d(4567)} + \\ + & \underbrace{\orange{P}(12)}_{\text{polarizability}} = - i \hcancel[red]{\int} \yellow{G}(\red{12}) \hcancel[red]{\Gamma(342)} \yellow{G}(\red{21}) \hcancel[red]{d(34)} + = - i \yellow{G}(12)\yellow{G}(21) + \\ + & \underbrace{\red{W}(12)}_{\text{screening}} = v(12) + \int v(13) \orange{P}(34) \red{W}(42) d(34) + \\ + & \underbrace{\violet{\Sigma}(12)}_{\text{self-energy}} = i \hcancel[red]{\int} \yellow{G}(\red{12}) \red{W}(\red{12}) \hcancel[red]{\Gamma(423) d(34)} + = i \yellow{G}(12) \red{W}(12) + \end{align*} + \end{block} + \end{column} + \end{columns} +\end{frame} +%----------------------------------------------------- +\begin{frame}{Dynamical Version of $GW$} + \begin{columns} + \begin{column}{0.6\textwidth} + \begin{block}{Quasiparticle equation (in a general setting)} + \begin{equation*} + \qty[ \underbrace{\blue{\bF}}_{\text{\blue{Fock matrix}}} + \underbrace{\violet{\bSig^{\GW}} \qty(\om = \eGW{p})}_{\text{\violet{dynamic self-energy}}} ] \SO{p}{\GW} + = \underbrace{\eGW{p}}_{\text{quasiparticle energies}} \SO{p}{\GW} + \end{equation*} + \end{block} + \end{column} + \begin{column}{0.4\textwidth} + \begin{block}{Practical issues} + \begin{itemize} + \bigskip + \item dynamic + \item highly non-linear + \item non-Hermitian + \end{itemize} + \end{block} + \end{column} + \end{columns} + \begin{block}{$GW$ self-energy} + \begin{equation*} + \violet{\Sigma_{pq}^{\GW}}(\om) + = \sum_{i\nu} \frac{\red{W_{pi}^{\nu}} \red{W_{qi}^{\nu}}}{\om - \eGW{i} + \orange{\Omega_{\nu}} - \underbrace{\ii \eta}_{\text{regularizer}}} + + \sum_{a\nu} \frac{\red{W_{pa}^{\nu}} \red{W_{qa}^{\nu}}}{\om - \eGW{a} - \underbrace{\orange{\Omega_{\nu}}}_{\text{\orange{RPA excitation}}} + \ii \eta} + \end{equation*} + \end{block} + \begin{block}{Screened two-electron integrals} + \begin{equation*} + \red{W_{pq}^{\nu}} = \sum_{ia}\ERI{pi}{qa}\underbrace{\orange{\qty(\bX+\bY)_{ia}^{\nu}}}_{\text{\orange{RPA eigenvectors}}} + \end{equation*} + \end{block} +\end{frame} +%----------------------------------------------------- + +%----------------------------------------------------- +\begin{frame}{One-Shot $GW$ or $G_0W_0$} + \begin{block}{$G_0W_0$ features} + \begin{itemize} + \item Diagonal approximation + \item A single loop of Hedin's equations + \end{itemize} + \end{block} + \begin{block}{Quasiparticle equation (assuming a HF starting point)} + \begin{align*} + \qq*{\underline{Dynamic version:}} & \om = \blue{\eHF{p}} + \underbrace{\violet{\Sig_{pp}^{\GW}}(\om)}_{\text{built with HF quantities}} + \\ + \qq*{\underline{Linearized (static) version:}} & \eGW{p} = \blue{\eHF{p}} + Z_p \violet{\Sig_{pp}^{\GW}}(\om = \blue{\eHF{p}}) + \qq{with} + Z_p = \underbrace{\qty[ 1 - \eval{\pdv{\violet{\Sig_{pp}^{\GW}}(\om)}{\om}}_{\om = \blue{\eHF{p}}} ]^{-1}}_{\text{renormalization factor}} + \end{align*} + \end{block} + \begin{block}{$G_0W_0$ issues} + \begin{itemize} + \item Highly starting point dependent + \end{itemize} + \end{block} +\end{frame} +%----------------------------------------------------- + + +%----------------------------------------------------- +\begin{frame}{Eigenvalue-Only $GW$ or ev$GW$} + \begin{block}{ev$GW$ features} + \begin{itemize} + \item Diagonal approximation + \item Self-consistency on the quasiparticle energies only + \end{itemize} + \end{block} + \begin{block}{Quasiparticle equation (assuming a HF starting point)} + \begin{align*} + \om = \blue{\eHF{p}} + \underbrace{\violet{\Sig_{pp}^{\GW}}(\om)}_{\text{built with $GW$ quantities}} + \end{align*} + \end{block} + \begin{block}{ev$GW$ issues} + \begin{itemize} + \item Lack of self-consistency on the orbitals + \item Challenging to converge (even with DIIS) + \end{itemize} + \end{block} +\end{frame} +%----------------------------------------------------- + +%----------------------------------------------------- +\begin{frame}{Quasiparticle Self-Consistent $GW$ or qs$GW$} + \begin{block}{qs$GW$ features} + \begin{itemize} + \item Static approximation of the self-energy + \item Brute-force symmetrization + \end{itemize} + \end{block} + \begin{block}{Quasiparticle equation} + \begin{equation*} + \qty[ \blue{\bF{}{}} + \underbrace{\purple{\bSig^{\qsGW}} }_{\text{static self-energy}} ] \SO{p}{\GW} + = \eGW{p} \SO{p}{\GW} + \qq{with} + \purple{\Sig_{pq}^{\qsGW}} = \underbrace{\frac{\violet{\Sig_{pq}^{\GW}}(\eGW{p}) + \violet{\Sig_{pq}^{\GW}}(\eGW{q})}{2}}_{\text{symmetrization}} + \end{equation*} + \pub{Faleev et al. PRL 93 (2004) 126406} + \end{block} + \begin{block}{qs$GW$ issues} + \begin{itemize} + \item ``Empirical'' symmetrization \pub{[Ismail-Beigi, JPCM 29 (2017) 385501]} + \item Very challenging to converge (even with DIIS) + \end{itemize} + \end{block} +\end{frame} +%----------------------------------------------------- + +%----------------------------------------------------- +\begin{frame}{Intruder-State Problem} + \begin{equation*} + \begin{split} + \text{\alert{Intruder-state problem}} + & \Leftrightarrow \text{a determinant in $\bQ$ becomes near-degenerate with a determinant in $\bP$} + \\ + & \Rightarrow \text{appearance of small denominators} + \\ + & \Rightarrow \text{\alert{convergence issues!}} + \\ + \\ + \text{How to avoid intruder states?} + & \Rightarrow \text{do not enforce $\bQ \bH^\text{eff} \bP = \bO$} + \\ + & \Leftrightarrow \text{near-degenerate determinants are not decoupled} + \\ + \end{split} + \end{equation*} + \begin{center} + \begin{tabular}{m{0.5\textwidth} b{0.5\textwidth}} + \includegraphics[width=0.5\textwidth]{fig/Heff_SRG} + & + $\Leftarrow$ \alert{Continuous (unitary) SRG transformation} + \end{tabular} + \end{center} + \alert{SRG decouples the Hamiltonian starting from states that have the largest energy separation and progressing to states with smaller energy separation} +\end{frame} +%----------------------------------------------------- + +%----------------------------------------------------- +\begin{frame}{Historical Overview of SRG} + \begin{itemize} + \item Introduced independently by + \bigskip + \begin{itemize} + \item Glazek and Wilson in quantum field theory + \pub{[PRD 48 (1993) 5863, ibid 49 (1994) 4214]} + \bigskip + \item Wegner in condensed matter systems + \pub{[Ann. Phys. 506 (1994) 77]} + \end{itemize} + \bigskip + \item (In-Medium) SRG is used a lot in nuclear physics + \\ + \pub{[Hergert et al. Phys. Rep. 621 (2016) 165]} + \bigskip + \item First introduced in chemistry by Steven White + \\ + \pub{[JCP 117 (2002) 7472]} + \bigskip + \item More recently developed by the group of Francesco Evangelista (SR/MR-DSRG) + \\ + \pub{[JCP 141 (2014) 054109; Annu. Rev. Phys. Chem. 70 (2019) 275]} + \end{itemize} +\end{frame} +%----------------------------------------------------- + +%----------------------------------------------------- +\begin{frame}{SRG Fundamental Equation} + \begin{block}{Unitary transformation of the Hamiltonian} + \begin{equation*} + \boxed{\bH \rightarrow \bH(s) = \bU(s) \, \bH \, \bU^\dag(s), \quad s \in [0,\infty)} + \end{equation*} + \begin{itemize} + \item For $s > 0$, $\bH(s)$ has a more (block) diagonal form than $\bH$ + \bigskip + \item The \alert{flow variable} $s$ is a time-like parameter that controls the extent of the transformation + \bigskip + \begin{itemize} + \item If $s = 0$, then $\bU(s) = \bI$, i.e., $\bH(s=0) = \bH$ + \bigskip + \item In the limit $s \to \infty$, $\bH(s)$ becomes (block) diagonal + \bigskip + \end{itemize} + \end{itemize} + \begin{equation*} + \bH(s) = \underbrace{\bH_\text{d}(s)}_{\text{diagonal}} + \underbrace{\bH_\text{od}(s)}_{\text{off-diagonal}} + \qq{$\Rightarrow$} + \lim_{s\to\infty} \bH_\text{od}(s) = 0 + \end{equation*} + \end{block} +\end{frame} +%----------------------------------------------------- + +%----------------------------------------------------- +\begin{frame}{SRG Flow Equation} + \begin{block}{The SRG flow equation} + \begin{equation*} + \label{eq:flow_eq} + \boxed{\dv{\bH(s)}{s} = \comm{\boldsymbol{\eta}(s)}{\bH(s)}, \quad \bH(0) = \bH} + \end{equation*} + \begin{equation*} + \qq*{where the \alert{flow generator}} + \boldsymbol{\eta}(s) = \dv{\bU(s)}{s} \bU^\dag(s) = - \boldsymbol{\eta}^\dag(s) + \qq{is an \alert{anti-Hermitian} operator} + \end{equation*} + \end{block} + \alert{Suitable parametrization of $\heta(s)$ allows to integrate the flow equation and find a numerical solution of $\hH(s)$ that satisfies the boundary conditions without having to explicitly construct $\hU(s)$} + \begin{block}{Wegner's canonical generator} + \begin{equation*} + \boxed{\boldsymbol{\eta}^\text{W}(s) = \comm{\bH_\text{d}(s)}{\bH_\text{od}(s)}} + \end{equation*} + \begin{equation*} + \qq*{As long as $\boldsymbol{\eta}^\text{W}(s) \neq 0$,} \dv{}{s} \Tr[\bH_\text{od}(s)^2] \le 0 + \qq{$\Rightarrow$ \alert{off-diagonal decreases in a monotonic way}} + \end{equation*} + \end{block} +\end{frame} +%----------------------------------------------------- + +%----------------------------------------------------- +\begin{frame}{Perturbative Analysis} + \begin{block}{Partitionning of the initial problem} + \begin{equation*} + \bH(s=0) + = \underbrace{\bH_\text{d}(s=0)}_{\text{\alert{zeroth order}}} + + \la \underbrace{\bH_\text{od}(s=0)}_{\text{\alert{first order}}} + \end{equation*} + \end{block} + \begin{block}{Perturbative analysis of the SRG equations} + \begin{align*} + \bH(s) & = \bH^{(0)}(s) + \la \bH^{(1)}(s) + \la^2 \bH^{(2)}(s) + \cdots + \\ + \boldsymbol{\eta}(s) + & = \boldsymbol{\eta}^{(0)}(s) + \la \boldsymbol{\eta}^{(1)}(s) + \la^2 \boldsymbol{\eta}^{(2)}(s) + \cdots + \end{align*} + \end{block} + \bigskip + \alert{How to identify the diagonal and off-diagonal terms in $GW$?} +\end{frame} +%----------------------------------------------------- + + + +%----------------------------------------------------- +\begin{frame}{Static Version of $GW$} + \begin{equation*} + \left. + \begin{array}{cc} + \qty[ \blue{\bF} + \violet{\bSig^{\GW}} \qty(\om = \eGW{p}) ] \SO{p}{\GW} = \eGW{p} \SO{p}{\GW} + \\ + \\ + \begin{split} + \violet{\bSig^{\GW}}(\om) + & = \red{\bW^{\text{2h1p}}} \qty(\om \bI - \orange{\bC^{\text{2h1p}}})^{-1} (\red{\bW^{\text{2h1p}}})^{\dag} + \\ + & + \red{\bW^{\text{2p1h}}} \qty(\om \bI - \orange{\bC^{\text{2p1h}}})^{-1} (\red{\bW^{\text{2p1h}}})^{\dag} + \end{split} + \end{array} + \right\} + \qq{$\xleftrightharpoons[\text{upfolding}]{\text{downfolding}}$} + \begin{cases} + \bH \Psi_{p}^{\GW} = \eGW{p} \Psi_{p}^{\GW} + \\ + \bH = + \begin{pmatrix} + \blue{\bF} & \red{\bW^{\text{2h1p}}} & \orange{\bW^{\text{2p1h}}} + \\ + (\red{\bW^{\text{2h1p}}})^\dag & \red{\bC^{\text{2h1p}}} & \bO + \\ + (\orange{\bW^{\text{2p1h}}})^\dag & \bO & \orange{\bC^{\text{2p1h}}} + \end{pmatrix} + \end{cases} + \end{equation*} + \begin{center} + \includegraphics[width=0.5\linewidth]{fig/upfolding} + \end{center} + \pub{Bintrim \& Berkelbach, JCP 154 (2021) 041101; Monino \& Loos JCP 156 (2022) 231101; Tolle \& Chan, arXiv:2212.08982} +\end{frame} +%----------------------------------------------------- + +%----------------------------------------------------- +\begin{frame}{Regularized Quasiparticle Equation} + \begin{block}{Regularized $GW$ equations up to second order} + \begin{equation*} + \qty[ \blue{\widetilde{\bF}}(s) + \magenta{\widetilde{\bSig}^{\SRGGW}}(\om = \eGW{p} ;s) ] \SO{p}{\GW} = \eGW{p} \SO{p}{\GW} + \end{equation*} + \end{block} + \begin{block}{Energy-dependent regularization} + \begin{equation*} + \blue{\widetilde{\bF}_{pq}}(s) = \delta_{pq} \blue{\eHF{p}} + + \sum_{r\nu} \frac{\Delta_{pr}^{\nu} + \Delta_{qr}^{\nu}}{(\Delta_{pr}^{\nu})^2 + (\Delta_{qr}^{\nu})^2 } + \qty[ \red{W_{pr}^{\nu}} \red{W_{qr}^{\nu}} - \purple{W_{pr}^{\nu}}(s) \purple{W_{qr}^{\nu}}(s) ] + \qq{with} + \Delta_{pr}^{\nu} = \eGW{p} - \eGW{r} \pm \Om_\nu + \end{equation*} + \begin{equation*} + \magenta{\widetilde{\Sigma}_{pq}^{\SRGGW}}(\om;s) + = \sum_{i\nu} \frac{\purple{W_{pi}^{\nu}}(s) \purple{W_{qi}^{\nu}}(s)}{\om - \eGW{i} + \Om_{\nu}} + + \sum_{a\nu} \frac{\purple{W_{pa}^{\nu}}(s) \purple{W_{qa}^{\nu}}(s)}{\om - \eGW{a} - \Om_{\nu}} + \qq{with} + \boxed{\purple{W_{pr}^{\nu}}(s) = \red{W_{pr}^{\nu}} e^{-(\Delta_{pr}^{\nu})^2 s}} + \end{equation*} + For a fixed value of the \alert{energy cut-off} $\Lambda = s^{-1/2}$, + \begin{align*} + \qif* \abs*{\Delta_{pr}^{\nu}} \gg \Lambda & \qthen & \purple{W_{pr}^{\nu}}(s) & = \red{W_{pr}^{\nu}} e^{-(\Delta_{pr}^{\nu})^2 s} \approx 0 & \qq{(decoupled)} + \\ + \qif* \abs*{\Delta_{pr}^{\nu}} \ll \Lambda & \qthen & \purple{W_{pr}^{\nu}}(s) & \approx \red{W_{pr}^{\nu}} & \qq{(remains coupled)} + \end{align*} + \end{block} +\end{frame} +%----------------------------------------------------- + +%----------------------------------------------------- +\begin{frame}{Limiting Forms} + \begin{block}{Limit as $s \to 0$} + \begin{equation*} + \blue{\widetilde{\bF}}(s=0) = \blue{\bF} + \qq{and} + \magenta{\widetilde{\bSig}^{\SRGGW}}(\om;s=0) = \violet{\bSig^{\GW}}(\om) + \end{equation*} + \end{block} + \begin{block}{Limit as $s \to \infty$} + \begin{equation*} + \magenta{\widetilde{\bSig}^{\SRGGW}}(\om;s\to\infty) = \bO + \qq{and} + \blue{\widetilde{F}_{pq}}(s\to\infty) + = \delta_{pq} \blue{\eHF{p}} + + \underbrace{\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}}}_{\text{static correction}} + \end{equation*} + \end{block} + \alert{By removing the coupling terms, SRG transforms continuously the dynamic problem into a static one} + \begin{block}{SRG-qs$GW$ self-energy from first principles} + \begin{equation*} + \cyan{\widetilde{\bSig}^{\SRGqsGW}}(\om;s) + = \sum_{r\nu} \frac{\Delta_{pr}^{\nu} + \Delta_{qr}^{\nu}}{(\Delta_{pr}^{\nu})^2 + (\Delta_{qr}^{\nu})^2 } + \qty[ \red{W_{pr}^{\nu}} \red{W_{qr}^{\nu}} - \purple{W_{pr}^{\nu}}(s) \purple{W_{qr}^{\nu}}(s) ] + \end{equation*} + \end{block} +\end{frame} +%----------------------------------------------------- + +%----------------------------------------------------- +\begin{frame}{SRG-qs$GW$} + \begin{center} + \includegraphics[width=0.9\textwidth]{fig/flow} + \end{center} +\end{frame} +%----------------------------------------------------- + +%----------------------------------------------------- +\begin{frame}{qs$GW$ vs SRG-qs$GW$ functional forms for $s=1/(2\eta^2)$} + \begin{center} + \includegraphics[width=0.9\textwidth]{fig/qs_vs_SRG} + \end{center} +\end{frame} +%----------------------------------------------------- + +%----------------------------------------------------- +\begin{frame}{Example: Principal IP of water (aug-cc-pVTZ) wrt $\Delta$CCSD(T)} + \begin{center} + \includegraphics[width=0.8\textwidth]{fig/water} + \end{center} +\end{frame} +%----------------------------------------------------- + +%----------------------------------------------------- +\begin{frame}{Principal IPs for a set of small molecules (aug-cc-pVTZ) wrt $\Delta$CCSD(T)} + \begin{center} + \includegraphics[width=\textwidth]{fig/IPs} + \end{center} + \begin{tabular}{p{1cm}p{3cm}p{3cm}p{3cm}p{3cm}} + MSE & 0.64 eV & 0.26 eV & 0.24 eV & 0.17 eV \\ + MAE & 0.74 eV & 0.32 eV & 0.25 eV & 0.19 eV \\ + \end{tabular} +\end{frame} +%----------------------------------------------------- + +%----------------------------------------------------- +\begin{frame}{Principal EAs for a set of small molecules (aug-cc-pVTZ) wrt $\Delta$CCSD(T)} + \begin{center} + \includegraphics[width=\textwidth]{fig/EAs} + \end{center} + \begin{tabular}{p{1cm}p{3cm}p{3cm}p{3cm}p{3cm}} + MSE & -0.30 eV & -0.02 eV & 0.00 eV & 0.00 eV \\ + MAE & 0.32 eV & 0.19 eV & 0.11 eV & 0.12 eV \\ + \end{tabular} +\end{frame} +%----------------------------------------------------- + +%----------------------------------------------------- +\begin{frame}{Acknowledgements \& Funding} + \begin{columns} + \begin{column}{0.5\textwidth} + \begin{itemize} + \item \textbf{Antoine Marie} + \item \textbf{Francesco Evangelista} + \item Enzo Monino + \item Roberto Orlando + \item Yann Damour + \item Sara Giarrusso + \item Ra\'ul Quintero-Monsebaiz + \item F\'abris Kossoski + \item Anthony Scemama + \item Michel Caffarel + \end{itemize} + \end{column} + \begin{column}{0.5\textwidth} + \centering + \includegraphics[width=0.8\textwidth]{fig/ERC} + \bigskip + \url{https://pfloos.github.io/WEB_LOOS} + \url{https://lcpq.github.io/PTEROSOR} + \bigskip + \end{column} + \end{columns} +\end{frame} +%----------------------------------------------------- + +\end{document} + + + +\end{document} diff --git a/Sanibel_2023/beamerbackgroundpterosor.png b/Sanibel_2023/beamerbackgroundpterosor.png new file mode 100644 index 0000000..560ba51 Binary files /dev/null and b/Sanibel_2023/beamerbackgroundpterosor.png differ diff --git a/Sanibel_2023/beamercolorthemepterosor.sty b/Sanibel_2023/beamercolorthemepterosor.sty new file mode 100644 index 0000000..8ac2304 --- /dev/null +++ b/Sanibel_2023/beamercolorthemepterosor.sty @@ -0,0 +1,33 @@ +\mode + +% Settings +\definecolor{myBlue}{RGB}{97,148,201} +\definecolor{myDarkBlue}{RGB}{73,110,150} +\definecolor{myPink}{RGB}{200,149,147} +\definecolor{myRed}{RGB}{206,51,45} + + +\setbeamercolor*{title page header}{fg=myRed} +\setbeamercolor*{author}{fg=myDarkBlue} +\setbeamercolor*{institute}{fg=myDarkBlue} +\setbeamercolor*{date}{fg=myBlue} + +\setbeamercolor*{item}{fg=myBlue} +\setbeamertemplate{items}[triangle] +\setbeamertemplate{sections/subsections in toc}[square] + +\setbeamercolor*{section title}{fg=myBlue} +\setbeamercolor*{subsection title}{fg=myBlue} +\setbeamercolor{block title}{fg=white,bg=myBlue} +%\setbeamercolor{block body}{bg=block title.bg!30!bg} + +% alertblock +\setbeamercolor{block title alerted}{fg=white,bg=MyPink} +%\setbeamercolor{block body alerted}{bg=block title alerted.bg!10!bg} + +% exampleblock +\setbeamercolor{block title example}{fg=myBlue} +%\setbeamercolor{block body example}{bg=white} + +\mode + diff --git a/Sanibel_2023/beamerfontthemepterosor.log b/Sanibel_2023/beamerfontthemepterosor.log new file mode 100644 index 0000000..c8cad2a --- /dev/null +++ b/Sanibel_2023/beamerfontthemepterosor.log @@ -0,0 +1,66 @@ +This is pdfTeX, Version 3.14159265-2.6-1.40.21 (TeX Live 2020) (preloaded format=pdflatex 2020.6.14) 10 DEC 2020 21:15 +entering extended mode + restricted \write18 enabled. + file:line:error style messages enabled. + %&-line parsing enabled. +**beamerfontthemepterosor.sty +(./beamerfontthemepterosor.sty +LaTeX2e <2020-02-02> patch level 5 +L3 programming layer <2020-06-03> + +LaTeX Warning: You have requested package `', + but the package provides `beamerfontthemepterosor'. + +Package: beamerfontthemepterosor 2020/12/10 pterosor font theme +(/usr/local/texlive/2020/texmf-dist/tex/latex/etoolbox/etoolbox.sty +Package: etoolbox 2019/09/21 v2.5h e-TeX tools for LaTeX (JAW) +\etb@tempcnta=\count167 +) +(/usr/local/texlive/2020/texmf-dist/tex/generic/iftex/ifxetex.sty +Package: ifxetex 2019/10/25 v0.7 ifxetex legacy package. 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A full list of +%% contributors can be found at +%% +%% https://github.com/matze/mtheme/graphs/contributors +%% +%% and the original template was based on the HSRM theme by Benjamin Weiss. +%% +%% This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 +%% International License (https://creativecommons.org/licenses/by-sa/4.0/). +%% --------------------------------------------------------------------------- +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{beamerfontthemepterosor}[2020/12/10 pterosor font theme] +\RequirePackage{etoolbox} +\RequirePackage{ifxetex} +\RequirePackage{ifluatex} +\RequirePackage{pgfopts} + +%\RequirePackage{mathpazo} +\RequirePackage{libertine} + +\ifboolexpr{bool {xetex} or bool {luatex}}{ + \@ifpackageloaded{fontspec}{ + \PassOptionsToPackage{no-math}{fontspec} + }{ + \RequirePackage[no-math]{fontspec} + } + \newcounter{fontsnotfound} + \newcommand{\checkfont}[1]{% + \suppressfontnotfounderror=1% + \font\x = "#1" at 10pt + \selectfont + 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item}{series=\bfseries} +\setbeamerfont{page number in head/foot}{size=\scriptsize} +\setbeamerfont{bibliography entry author}{size=\normalsize,% + series=\normalfont} +\setbeamerfont{bibliography entry title}{size=\normalsize,% + series=\bfseries} +\setbeamerfont{bibliography entry location}{size=\normalsize,% + series=\normalfont} +\setbeamerfont{bibliography entry note}{size=\small,% + series=\normalfont} +\setbeamerfont{standout}{size=\Large,% + series=\bfseries} +\pgfkeys{ + /pterosor/font/titleformat title/.cd, + .is choice, + regular/.code={% + \let\pterosor@titleformat\@empty% + \setbeamerfont{title}{shape=\normalfont}% + }, + smallcaps/.code={% + \let\pterosor@titleformat\@empty% + \setbeamerfont{title}{shape=\scshape}% + }, + allsmallcaps/.code={% + \let\pterosor@titleformat\lowercase% + \setbeamerfont{title}{shape=\scshape}% + \PackageWarning{beamerthemepterosor}{% + Be aware that titleformat title=allsmallcaps can lead to problems% + } + }, + allcaps/.code={% + \let\pterosor@titleformat\uppercase% + \setbeamerfont{title}{shape=\normalfont} + \PackageWarning{beamerthemepterosor}{% + Be aware that titleformat title=allcaps can lead to problems% + } + }, +} +\pgfkeys{ + /pterosor/font/titleformat subtitle/.cd, + .is choice, + regular/.code={% + \let\pterosor@subtitleformat\@empty% + \setbeamerfont{subtitle}{shape=\normalfont}% + }, + smallcaps/.code={% + \let\pterosor@subtitleformat\@empty% + \setbeamerfont{subtitle}{shape=\scshape}% + }, + allsmallcaps/.code={% + \let\pterosor@subtitleformat\lowercase% + \setbeamerfont{subtitle}{shape=\scshape}% + \PackageWarning{beamerthemepterosor}{% + Be aware that titleformat subtitle=allsmallcaps can lead to problems% + } + }, + allcaps/.code={% + \let\pterosor@subtitleformat\uppercase% + \setbeamerfont{subtitle}{shape=\normalfont}% + \PackageWarning{beamerthemepterosor}{% + Be aware that titleformat subtitle=allcaps can lead to problems% + } + }, +} +\pgfkeys{ + /pterosor/font/titleformat section/.cd, + .is choice, + regular/.code={% + \let\pterosor@sectiontitleformat\@empty% + \setbeamerfont{section title}{shape=\normalfont}% + }, + smallcaps/.code={% + \let\pterosor@sectiontitleformat\@empty% + \setbeamerfont{section title}{shape=\scshape}% + }, + allsmallcaps/.code={% + \let\pterosor@sectiontitleformat\MakeLowercase% + \setbeamerfont{section title}{shape=\scshape}% + \PackageWarning{beamerthemepterosor}{% + Be aware that titleformat section=allsmallcaps can lead to problems% + } + }, + allcaps/.code={% + \let\pterosor@sectiontitleformat\MakeUppercase% + \setbeamerfont{section title}{shape=\normalfont}% + \PackageWarning{beamerthemepterosor}{% + Be aware that titleformat section=allcaps can lead to problems% + } + }, +} +\pgfkeys{ + /pterosor/font/titleformat frame/.cd, + .is choice, + regular/.code={% + \let\pterosor@frametitleformat\@empty% + \setbeamerfont{frametitle}{shape=\normalfont}% + }, + smallcaps/.code={% + \let\pterosor@frametitleformat\@empty% + \setbeamerfont{frametitle}{shape=\scshape}% + }, + allsmallcaps/.code={% + \let\pterosor@frametitleformat\MakeLowercase% + \setbeamerfont{frametitle}{shape=\scshape}% + \PackageWarning{beamerthemepterosor}{% + Be aware that titleformat frame=allsmallcaps can lead to problems% + } + }, + allcaps/.code={% + \let\pterosor@frametitleformat\MakeUppercase% + \setbeamerfont{frametitle}{shape=\normalfont} + \PackageWarning{beamerthemepterosor}{% + Be aware that titleformat frame=allcaps can lead to problems% + } + }, +} +\pgfkeys{ + /pterosor/font/.cd, + titleformattitle/.code=\pgfkeysalso{titleformat title=#1}, + titleformatsubtitle/.code=\pgfkeysalso{titleformat subtitle=#1}, + titleformatsection/.code=\pgfkeysalso{titleformat section=#1}, + titleformatframe/.code=\pgfkeysalso{titleformat frame=#1}, +} +\newcommand{\pterosor@font@setdefaults}{ + \pgfkeys{/pterosor/font/.cd, + titleformat title=regular, + titleformat subtitle=regular, + titleformat section=regular, + titleformat frame=regular, + } +} +\def\pterosor@titleformat#1{#1} +\def\pterosor@subtitleformat#1{#1} +\def\pterosor@sectiontitleformat#1{#1} +\def\pterosor@frametitleformat#1{#1} +\patchcmd{\beamer@title}% + {\def\inserttitle{#2}}% + {\def\inserttitle{\pterosor@titleformat{#2}}}% + {}% + {\PackageError{beamerfontthemepterosor}{Patching title failed}\@ehc} +\patchcmd{\beamer@subtitle}% + {\def\insertsubtitle{#2}}% + {\def\insertsubtitle{\pterosor@subtitleformat{#2}}}% + {}% + {\PackageError{beamerfontthemepterosor}{Patching subtitle failed}\@ehc} +\patchcmd{\sectionentry} + {\def\insertsectionhead{#2}} + {\def\insertsectionhead{\pterosor@sectiontitleformat{#2}}} + {} + {\PackageError{beamerfontthemepterosor}{Patching section title failed}\@ehc} +\@tempswafalse +\patchcmd{\beamer@section} + {\def\insertsectionhead{\hyperlink{Navigation\the\c@page}{#1}}} + {\def\insertsectionhead{\hyperlink{Navigation\the\c@page}{% + \pterosor@sectiontitleformat{#1}}}} + {\@tempswatrue} + {} +\patchcmd{\beamer@section} + {\protected@edef\insertsectionhead{\noexpand\hyperlink{Navigation\the\c@page}{#1}}} + {\protected@edef\insertsectionhead{\noexpand\hyperlink{Navigation\the\c@page}{% + \noexpand\pterosor@sectiontitleformat{#1}}}} + {\@tempswatrue} + {} +\if@tempswa\else + \PackageError{beamerfontthemepterosor}{Patching section title failed}\@ehc +\fi +\@tempswafalse +\patchcmd{\beamer@subsection} + {\def\insertsubsectionhead{\hyperlink{Navigation\the\c@page}{#1}}} + {\def\insertsubsectionhead{\hyperlink{Navigation\the\c@page}{% + \pterosor@sectiontitleformat{#1}}}} + {\@tempswatrue} + {} +\patchcmd{\beamer@subsection} + {\protected@edef\insertsubsectionhead{\noexpand\hyperlink{Navigation\the\c@page}{#1}}} + {\protected@edef\insertsubsectionhead{\noexpand\hyperlink{Navigation\the\c@page}{% + \noexpand\pterosor@sectiontitleformat{#1}}}} + {\@tempswatrue} + {} +\if@tempswa\else + \PackageError{beamerfontthemepterosor}{Patching section title failed}\@ehc +\fi +\patchcmd{\beamer@@frametitle} + {{% + \gdef\insertframetitle{{#2\ifnum\beamer@autobreakcount>0\relax{}\space% + \usebeamertemplate*{frametitle continuation}\fi}}% + \gdef\beamer@frametitle{#2}% + \gdef\beamer@shortframetitle{#1}% + }} + {{% + \gdef\insertframetitle{{\pterosor@frametitleformat{#2}\ifnum% + \beamer@autobreakcount>0\relax{}\space% + \usebeamertemplate*{frametitle continuation}\fi}}% + \gdef\beamer@frametitle{#2}% + \gdef\beamer@shortframetitle{#1}% + }} + {} + {\PackageError{beamerfontthemepterosor}{Patching frame title failed}\@ehc} +\pterosor@font@setdefaults +\ProcessPgfPackageOptions{/pterosor/font} +\endinput +%% +%% End of file `beamerfontthemepterosor.sty'. diff --git a/Sanibel_2023/beamerinnerthemepterosor.sty b/Sanibel_2023/beamerinnerthemepterosor.sty new file mode 100644 index 0000000..7f657f3 --- /dev/null +++ b/Sanibel_2023/beamerinnerthemepterosor.sty @@ -0,0 +1,53 @@ +\mode + +\setbeamertemplate{background}{ +\ifnum\thepage>1 +\includegraphics[height=\paperheight]{beamerbackgroundpterosor.png} +\else +\includegraphics[height=\paperheight]{beamertitlepterosor.png} +\fi +} + +% Title page +\defbeamertemplate*{title page}{pterosor}[1][] +{ + \vskip3cm% + \begin{beamercolorbox}[wd=6.cm,leftskip=-0.5cm,#1]{title page header} + \usebeamerfont{title}\inserttitle\par% + \end{beamercolorbox}% + \vskip0.2cm% + \begin{beamercolorbox}[wd=6.cm,leftskip=-0.5cm,#1]{author} + \usebeamerfont{author}\insertauthor% + \end{beamercolorbox} + \vskip0.3cm% + \begin{beamercolorbox}[wd=6.cm,leftskip=-0.5cm,#1]{date} + \usebeamerfont{author}\insertdate% + \end{beamercolorbox} + \vskip0.3cm% + \begin{beamercolorbox}[wd=7.cm,leftskip=-0.5cm,#1]{institute} + \usebeamerfont{author}{\tiny \insertinstitute}% + \end{beamercolorbox} + \vfill +} + +% Section page +\defbeamertemplate*{section page}{pterosor}{ + \centering + \begin{minipage}{22em} + \raggedright + \usebeamercolor[fg]{section title} + \usebeamerfont{section title} + \insertsectionhead\\[-1ex] + \par + \ifx\insertsubsectionhead\@empty\else% + \usebeamercolor[fg]{subsection title}% + \usebeamerfont{subsection title}% + \insertsubsectionhead + \fi + \end{minipage} + \par + \vspace{\baselineskip} +} + + +\mode diff --git a/Sanibel_2023/beamerouterthemepterosor.sty b/Sanibel_2023/beamerouterthemepterosor.sty new file mode 100644 index 0000000..57362a0 --- /dev/null +++ b/Sanibel_2023/beamerouterthemepterosor.sty @@ -0,0 +1,20 @@ +\mode + +% Frame title +\defbeamertemplate*{frametitle}{pterosor}[1][] +{ + \begin{beamercolorbox}[wd=\paperwidth,ht=0.95cm]{frametitle} + \begin{tikzpicture} +% \useasboundingbox[fill=white](0,0) rectangle(\the\paperwidth,1.); +%\fill[red!80!black] (0,0) rectangle(2.95,1.); +%\fill[blue!50!cyan!80!black] (3.05,0) rectangle(\the\paperwidth,1.); +%\fill[white!50] (3.05,0) rectangle(\the\paperwidth,1.); + \useasboundingbox[](0,0) rectangle(\the\paperwidth,1.); + \node[anchor=east, white,font=\large] at + (\paperwidth,0.25){\insertframetitle \phantom{m}}; + \end{tikzpicture} + \end{beamercolorbox} +} + +\mode + diff --git a/Sanibel_2023/beamerthemepterosor.sty b/Sanibel_2023/beamerthemepterosor.sty new file mode 100644 index 0000000..8aad8a8 --- /dev/null +++ b/Sanibel_2023/beamerthemepterosor.sty @@ -0,0 +1,29 @@ +\mode + + +% Requirement +\RequirePackage{tikz} + +% Settings +\useinnertheme{pterosor} +\useoutertheme{pterosor} +\usecolortheme{pterosor} +\usefonttheme{pterosor} + + +% we remove the navigation symbols and define blocks aspect. +\setbeamertemplate{navigation symbols}{} +\setbeamertemplate{blocks}[rounded][shadow=true] + +\AtBeginSection[]{% + \begin{frame}[plain] + \usebeamertemplate{section page} + \end{frame} +} + +\setbeamertemplate{footline}{ + \vspace{0.6cm} +} + + +\mode diff --git a/Sanibel_2023/beamertitlepterosor.png b/Sanibel_2023/beamertitlepterosor.png new file mode 100644 index 0000000..a851df0 Binary files /dev/null and b/Sanibel_2023/beamertitlepterosor.png 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mode 100644 index 0000000..e28df55 Binary files /dev/null and b/Sanibel_2023/fig/hH_EE.png differ diff --git a/Sanibel_2023/fig/pentagon.tex b/Sanibel_2023/fig/pentagon.tex new file mode 100644 index 0000000..cb890a6 --- /dev/null +++ b/Sanibel_2023/fig/pentagon.tex @@ -0,0 +1,61 @@ +\documentclass{standalone} + +\usepackage{graphicx,bm,microtype,hyperref,algpseudocode,subfigure,algorithm,algorithmicx,multirow,footnote,xcolor,physics,lipsum,wasysym} + +\definecolor{darkgreen}{RGB}{0, 180, 0} +\newcommand{\red}[1]{\textcolor{red}{#1}} +\newcommand{\purple}[1]{\textcolor{purple}{#1}} +\newcommand{\orange}[1]{\textcolor{orange}{#1}} +\newcommand{\green}[1]{\textcolor{darkgreen}{#1}} +\newcommand{\blue}[1]{\textcolor{blue}{#1}} +\newcommand{\pub}[1]{\textcolor{purple}{#1}} +\newcommand{\violet}[1]{\textcolor{violet}{#1}} + +\usepackage{tikz} +\usetikzlibrary{arrows,positioning,shapes.geometric} +\usetikzlibrary{decorations.pathmorphing} +\usetikzlibrary{decorations.pathreplacing} + +\tikzset{snake it/.style={ +decoration={snake, + amplitude = .4mm, + segment length = 2mm},decorate} +} + +\begin{document} + +%%% FIGURE 1 %%% +\begin{tikzpicture} + \begin{scope}[very thick, + node distance=2.5cm,on grid,>=stealth', + GOp/.style={circle,draw,fill=yellow!40}, + POp/.style={circle,draw,fill=orange!40}, + WOp/.style={circle,draw,fill=red!40}, + SigOp/.style={circle,draw,fill=violet!40}, + DeadOp/.style={circle,draw,fill=gray!40}, + Input/.style={fill=white!40}, + Output/.style={fill=white!40}] + + \node [GOp, align=center] (G) at (3*0.587785, 3*0.809017) {$G$}; + \node [DeadOp, align=center] (Gamma) at (3*0.951057, -3*0.309017) {$\Gamma$}; + \node [POp, align=center] (P) at (3*0, -3*1.00000) {$P$}; + \node [WOp, align=center] (W) at (-3*0.951057, -3*0.309017) {$W$}; + \node [SigOp, align=center] (Sigma) at (-3*0.587785, 3*0.809017) {$\Sigma$}; + \node [Input, align=center] (In) [above=of G] {}; + \node [Output, align=center] (Out) [above=of Sigma] {}; + \node [Input, align=center] (In) [above=of G] {In}; + \node [Output, align=center] (Out) [above=of Sigma] {Out}; + \path + (G) edge [->,color=black] node [above,sloped,black] {$\Gamma = 1 + \fdv{\Sigma}{G} GG \Gamma$} (Gamma) + (Gamma) edge [->,color=black] node [below,sloped,black] {$P = - i GG \Gamma$} (P) + (P) edge [->,color=black] node [above,sloped,black] {$W = v + vPW$} (W) + (W) edge [->,color=black] node [above,sloped,black] {$\Sigma = i GW\Gamma$} (Sigma) + (Sigma) edge [->,color=black] node [above,sloped,black] {$G = G_0 + G_0 \Sigma G$} (G) + (In) edge [->,color=black] node [above,sloped,black] {$\varepsilon^\text{HF/KS}$} (G) + (Sigma) edge [->,color=black] node [above,sloped,black] {$\varepsilon^{GW\Gamma}$} (Out) + ; + \end{scope} +\end{tikzpicture} +%%% %%% + +\end{document} diff --git a/Sanibel_2023/fig/qp2.png b/Sanibel_2023/fig/qp2.png new file mode 100644 index 0000000..f15ded9 Binary files /dev/null and b/Sanibel_2023/fig/qp2.png differ diff --git a/Sanibel_2023/fig/qs_vs_SRG.pdf b/Sanibel_2023/fig/qs_vs_SRG.pdf new file mode 100644 index 0000000..207454e Binary files /dev/null and b/Sanibel_2023/fig/qs_vs_SRG.pdf differ diff --git a/Sanibel_2023/fig/square.tex b/Sanibel_2023/fig/square.tex new file mode 100644 index 0000000..394999d --- /dev/null +++ b/Sanibel_2023/fig/square.tex @@ -0,0 +1,62 @@ +\documentclass{standalone} + +\usepackage{graphicx,bm,microtype,hyperref,algpseudocode,subfigure,algorithm,algorithmicx,multirow,footnote,xcolor,physics,lipsum,wasysym} + +\definecolor{darkgreen}{RGB}{0, 180, 0} +\newcommand{\red}[1]{\textcolor{red}{#1}} +\newcommand{\purple}[1]{\textcolor{purple}{#1}} +\newcommand{\orange}[1]{\textcolor{orange}{#1}} +\newcommand{\green}[1]{\textcolor{darkgreen}{#1}} +\newcommand{\blue}[1]{\textcolor{blue}{#1}} +\newcommand{\pub}[1]{\textcolor{purple}{#1}} +\newcommand{\violet}[1]{\textcolor{violet}{#1}} + +\usepackage{tikz} +\usetikzlibrary{arrows,positioning,shapes.geometric} +\usetikzlibrary{decorations.pathmorphing} +\usetikzlibrary{decorations.pathreplacing} + +\tikzset{snake it/.style={ +decoration={snake, + amplitude = .4mm, + segment length = 2mm},decorate} +} + +\begin{document} + +%%% FIGURE 1 %%% +\begin{tikzpicture} + \begin{scope}[very thick, + node distance=2.5cm,on grid,>=stealth', + GOp/.style={circle,draw,fill=yellow!40}, + POp/.style={circle,draw,fill=orange!40}, + WOp/.style={circle,draw,fill=red!40}, + SigOp/.style={circle,draw,fill=violet!40}, + DeadOp/.style={circle,draw,fill=gray!40,opacity=0.4}, + Input/.style={fill=white!40}, + Output/.style={fill=white!40}] + + \node [GOp, align=center] (G) at (3*0.587785, 3*0.809017) {$G$}; + \node [DeadOp, align=center] (Gamma) at (3*0.951057, -3*0.309017) {$\Gamma$}; + \node [POp, align=center] (P) at (3*0, -3*1.00000) {$P$}; + \node [WOp, align=center] (W) at (-3*0.951057, -3*0.309017) {$W$}; + \node [SigOp, align=center] (Sigma) at (-3*0.587785, 3*0.809017) {$\Sigma$}; + \node [Input, align=center] (In) [above=of G] {}; + \node [Output, align=center] (Out) [above=of Sigma] {}; + \node [Input, align=center] (In) [above=of G] {In}; + \node [Output, align=center] (Out) [above=of Sigma] {Out}; + \path + (G) edge [->,color=gray!50] node [above,sloped,gray!50] {$\Gamma = 1 + \fdv{\Sigma}{G} GG \Gamma$} (Gamma) + (Gamma) edge [->,color=gray!50] node [below,sloped,gray!50] {$P = - i GG \Gamma$} (P) + (P) edge [->,color=black] node [above,sloped,black] {$W = v + vPW$} (W) + (W) edge [->,color=black] node [above,sloped,black] {$\Sigma = i GW$} (Sigma) + (Sigma) edge [->,color=black] node [above,sloped,black] {$G = G_0 + G_0 \Sigma G$} (G) + (G) edge [->,color=black] node [above,sloped,black] {$P = - i GG$} (P) + (In) edge [->,color=black] node [above,sloped,black] {$\varepsilon^\text{HF/KS}$} (G) + (Sigma) edge [->,color=black] node [above,sloped,black] {$\varepsilon^\text{GW}$} (Out) + ; + \end{scope} +\end{tikzpicture} +%%% %%% + +\end{document} diff --git a/Sanibel_2023/fig/upfolding.tex b/Sanibel_2023/fig/upfolding.tex new file mode 100644 index 0000000..fe41c1e --- /dev/null +++ b/Sanibel_2023/fig/upfolding.tex @@ -0,0 +1,77 @@ +\documentclass{standalone} + +\usepackage{graphicx,bm,microtype,hyperref,algpseudocode,subfigure,algorithm,algorithmicx,multirow,footnote,xcolor,physics,lipsum,wasysym} + +\definecolor{darkgreen}{RGB}{0, 180, 0} +\newcommand{\red}[1]{\textcolor{red}{#1}} +\newcommand{\purple}[1]{\textcolor{purple}{#1}} +\newcommand{\orange}[1]{\textcolor{orange}{#1}} +\newcommand{\green}[1]{\textcolor{darkgreen}{#1}} +\newcommand{\black}[1]{\textcolor{black}{#1}} +\newcommand{\blue}[1]{\textcolor{blue}{#1}} +\newcommand{\pub}[1]{\textcolor{purple}{#1}} +\newcommand{\violet}[1]{\textcolor{violet}{#1}} + +\usepackage{tikz} +\usetikzlibrary{arrows,positioning,shapes.geometric} +\usetikzlibrary{decorations.pathmorphing} +\usetikzlibrary{decorations.pathreplacing} + +\tikzset{snake it/.style={ +decoration={snake, + amplitude = .4mm, + segment length = 2mm},decorate} +} + +\begin{document} + +%%% FIGURE 1 %%% +\begin{tikzpicture} + \begin{scope}[very thick, + node distance=2.5cm,on grid,>=stealth', + Operator/.style={circle,draw,fill=yellow!40}, + DeadOp/.style={circle,draw,fill=gray!40}, + Input/.style={fill=white!40}, + Output/.style={fill=white!40}] + + % model space + \draw [blue] (0,3.3) -- (1.1,3.3) -- (1.1,2.2) -- (0,2.2) -- (0,3.3); + \node [blue,thick] (model) at (0.55,2.75) {$\boldsymbol{F}$}; + % perturbative space + \draw [red] (0,3.3) -- (2.2,3.3) -- (2.2,1.1) -- (0,1.1) -- (0,3.3); + \node [thick] (model) at (1.65,1.65) {$\red{\boldsymbol{C}^{\text{2h1p}}}$}; + \node [thick] (model) at (1.65,2.75) {$\red{\boldsymbol{W}^{\text{2h1p}}}$}; + \node [thick] (model) at (0.55,1.65) {$\red{\boldsymbol{W}^{\text{2h1p}}}$}; + % FCI space + \draw [orange] (0,3.3) -- (3.3,3.3) -- (3.3,0) -- (0,0); + \draw [black] (0,0) -- (0,3.3) -- (3.3,3.3); + \node [thick] (model) at (2.75,0.55) {$\orange{\boldsymbol{C}^{\text{2p1h}}}$}; + \node [thick] (model) at (2.75,2.75) {$\orange{\boldsymbol{W}^{\text{2p1h}}}$}; + \node [thick] (model) at (0.55,0.55) {$\orange{\boldsymbol{W}^{\text{2p1h}}}$}; + \node [thick] (model) at (2.75,1.65) {$\black{\boldsymbol{0}}$}; + \node [thick] (model) at (1.65,0.55) {$\black{\boldsymbol{0}}$}; + \draw[step=1.1,black,thin] (0,0) grid (3.3,3.3); + + \draw [decorate,decoration={brace,amplitude=3pt},xshift=3pt,yshift=0] + (3.3,3.3) -- (3.3,2.2) node [black,midway,xshift=1.3cm] {\footnotesize internal space $\boldsymbol{P}$}; + + \draw [decorate,decoration={brace,mirror,amplitude=3pt},xshift=-3pt,yshift=0] + (0,3.3) -- (0,2.2) node [blue,midway,xshift=-1.3cm] {\footnotesize \blue{1h \& 1p conf.}}; + + \draw [decorate,decoration={brace,mirror,amplitude=3pt},xshift=-3pt,yshift=0] + (0,2.2) -- (0,1.1) node [black,midway,xshift=-1.3cm] {\footnotesize \red{2h1p conf.}}; + + \draw [decorate,decoration={brace,mirror,amplitude=3pt},xshift=-3pt,yshift=0] + (0,1.1) -- (0,0) node [black,midway,xshift=-1.3cm] {\footnotesize \orange{2p1h conf.}}; + + \draw [decorate,decoration={brace,amplitude=3pt},xshift=3pt,yshift=0pt] + (3.3,2.2) -- (3.3,0) node [black,midway,xshift=1.3cm] {\footnotesize external space $\boldsymbol{Q}$}; + +% \draw [decorate,decoration={brace,mirror,amplitude=3pt},xshift=0pt,yshift=-3pt] +% (0,0) -- (3,0) node [black,midway,yshift=-0.3cm] {\footnotesize FCI space}; + + \end{scope} +\end{tikzpicture} +%%% %%% + +\end{document} diff --git a/Sanibel_2023/fig/water.pdf b/Sanibel_2023/fig/water.pdf new file mode 100644 index 0000000..cac3af7 Binary files /dev/null and b/Sanibel_2023/fig/water.pdf differ