From 3e995e464000db7427de6d191190621b5f14c2de Mon Sep 17 00:00:00 2001
From: Antoine MARIE <amarie@irsamc.ups-tlse.fr>
Date: Mon, 14 Nov 2022 14:25:20 +0100
Subject: [PATCH] small changes

---
 Slides/SRG-GF.tex | 66 ++++++++++++++++++++++++-----------------------
 1 file changed, 34 insertions(+), 32 deletions(-)

diff --git a/Slides/SRG-GF.tex b/Slides/SRG-GF.tex
index 3ce594e..6c61360 100644
--- a/Slides/SRG-GF.tex
+++ b/Slides/SRG-GF.tex
@@ -104,27 +104,27 @@
 %-----------------------------------------------------
 \begin{frame}{Perturbative Expansions}
 	%
-	\begin{block}{Perturbative partitioning in the SRG framework}
-        \begin{equation}
-        	\bH(s) =
-            \underbrace{
-            \begin{pmatrix}
-            	\bF(s) & \bO 
-				\\
-            	\bO		& \bC(s) 
-            \end{pmatrix}
-            }_{\bHd{}(s)}
-            + \la
-			\underbrace{
-			\begin{pmatrix}
-				\bO				& \bV(s) 
-				\\
-            	\bV^{\dagger}(s)	& \bO
-			\end{pmatrix}
-			}_{\bHod(s)}
-       \end{equation}
-	\end{block}
-	\begin{block}{Components of the Hamiltonian}
+       %  \begin{block}{Perturbative partitioning in the SRG framework}
+       %  \begin{equation}
+       %  	\bH(s) =
+       %      \underbrace{
+       %      \begin{pmatrix}
+       %      	\bF(s) & \bO 
+       %  			\\
+       %      	\bO		& \bC(s) 
+       %      \end{pmatrix}
+       %      }_{\bHd{}(s)}
+       %      + \la
+       %  		\underbrace{
+       %  		\begin{pmatrix}
+       %  			\bO				& \bV(s) 
+       %  			\\
+       %      	\bV^{\dagger}(s)	& \bO
+       %  		\end{pmatrix}
+       %  		}_{\bHod(s)}
+       % \end{equation}
+       %  \end{block}
+	\begin{block}{Components of the effective Hamiltonian}
           \begin{subequations}
             \begin{align}
               \bH(s) & = \bH^{(0)}(s) + \la \bH^{(1)}(s) + \la^2 \bH^{(2)}(s) + \cdots
@@ -159,7 +159,7 @@
     \end{equation}	
   \end{block}
 	%
-	\begin{block}{Zeroth-order Hamiltonian}
+	\begin{block}{Zeroth-order effective Hamiltonian}
         \begin{equation}
 			\dv{\bH^{(0)}(s)}{s} 
 			= \comm{\bEta^{(0)}(s)}{\bH^{(0)}(s)} 
@@ -188,7 +188,7 @@
   		\end{equation}	
  	\end{block}
 	%
-	\begin{block}{First-order Hamiltonian}
+	\begin{block}{First-order effective Hamiltonian}
 		\begin{equation}
 			\dv{\bH^{(1)}}{s} 
 			= \comm{\bEta^{(0)}}{\bH^{(1)}} 
@@ -234,7 +234,7 @@
 			\boxed{\bC^{(1)}(s) = \bO}
 		\end{equation}
 	\end{block}
-	%
+	\pause[2]
 	\begin{block}{Off-diagonal terms}
 		\begin{gather}
 			\dv{\bV^{(1)}}{s} 
@@ -270,7 +270,7 @@
   		\end{equation}	
  	\end{block}
 	%
-	\begin{block}{Second-order Hamiltonian}
+	\begin{block}{Second-order effective Hamiltonian}
 		\begin{equation}
 			\dv{\bH^{(2)}}{s} 
 			= \comm{\bEta^{(2)}}{\bHd^{(0)}} + \underbrace{\comm{\bEta^{(1)}}{\bHd^{(1)}}}_{\bO}
@@ -316,7 +316,8 @@
 			= \sum_{rm} \frac{\Delta_{pr}^{m} + \Delta_{qr}^{m}}{(\Delta_{pr}^{m})^2 + (\Delta_{qr}^{m})^2 } 
 			W_{pr,m}^{(1)}(0) W_{qr,m}^{(1)}(0) \qty[ 1 - e^{-(\Delta_{pr}^{m})^2s} e^{-(\Delta_{qr}^{m})^2s} ] 
 		\end{gather}
-	\end{block}
+              \end{block}
+              \pause[2]
 	\begin{block}{Off-diagonal terms}
 		\begin{equation}
 			\dv{\bV^{(2)}}{s} 
@@ -332,12 +333,13 @@
 
 %-----------------------------------------------------
 \begin{frame}{Regularized Quasiparticle Equation}
-	\begin{block}{Regularized $GW$ equations up to second order}
-		\begin{equation}
-    		\qty[ \Tilde{\bF}(s) + \Tilde{\bSig}(\om;s) ] \bpsi = \om \bpsi
-		\end{equation}
-	\end{block}
-	\begin{block}{Regularized Fock elements}
+  \begin{block}{Regularized $GW$ equations up to second order}
+    \begin{equation}
+      \qty[ \Tilde{\bF}(s) + \Tilde{\bSig}(\om;s) ] \bpsi = \om \bpsi
+    \end{equation}
+  \end{block}
+  \pause[2]
+  \begin{block}{Regularized Fock elements}
 		\begin{equation}
 				\Tilde{\bF}(s) = \bF + \bF^{(2)}(s)
                 \qq{with}