From aef4f70ece8d7c3b966a18e0a96e707647055fa0 Mon Sep 17 00:00:00 2001
From: Stefan Gehr <stefan.kerman.gehr@fau.de>
Date: Sun, 11 Dec 2022 00:05:18 +0100
Subject: [PATCH] loop updates

---
 figures/graphmap.pdf              |  Bin 0 -> 80058 bytes
 figures/graphmap.svg              | 3171 +++++++++++++++++++++++++++++
 src/qmc-loop-algorithm-report.tex |   15 +-
 3 files changed, 3183 insertions(+), 3 deletions(-)
 create mode 100644 figures/graphmap.pdf
 create mode 100644 figures/graphmap.svg

diff --git a/figures/graphmap.pdf b/figures/graphmap.pdf
new file mode 100644
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diff --git a/figures/graphmap.svg b/figures/graphmap.svg
new file mode 100644
index 0000000..6c18f00
--- /dev/null
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diff --git a/src/qmc-loop-algorithm-report.tex b/src/qmc-loop-algorithm-report.tex
index cb05c50..9629c9f 100644
--- a/src/qmc-loop-algorithm-report.tex
+++ b/src/qmc-loop-algorithm-report.tex
@@ -81,7 +81,6 @@
 	{\color{lightgray} All possible configurations} \\
 	{\color{red} Significant configurations}
 	\end{minipage}
-	% TODO Tikz circle in circle
 \end{block}
 \begin{block}{Detailed Balance condition}
 	\begin{align*}
@@ -151,7 +150,7 @@
 	Accept with probability
 	\begin{align*}
 		\min\left(1, e^{-\num{0.1} \times \left[4 - (-4)\right]}\right) = e^{-\num{0.8}} \approx \num{0.45} \\
-		\die{} = \num{0.63} > \num{0.45} \Rightarrow \text{decline} \Rightarrow \vec{\sigma}_1 = \vec{\sigma}_0 = \uparrow\uparrow\downarrow\uparrow
+		\die{} = \num{0.63} > \num{0.45} \Rightarrow \text{decline}
 	\end{align*}
 }
 \visible<6->{
@@ -159,7 +158,7 @@
 	\begin{align*}
 		H(\uparrow\uparrow\uparrow\uparrow) = -12 \\
 		\min\left(1, e^{-\num{0.1}\times \left[-12 - (-4)\right]}\right) = \min(1, e^{\num{1.6}}) = 1 \\
-		\die{} \le 1 \Rightarrow \text{accept} \implies \vec{\sigma}_2 = \uparrow\uparrow\uparrow\uparrow
+		\die{} \le 1 \Rightarrow \text{accept}
 	\end{align*}
 }
 \end{minipage}
@@ -240,6 +239,8 @@ Always accept the new configuration
 \section{Quantum Monte Carlo}
 \subsection{XXZ Quantum Spin Chain}
 \subsection{Trotter Decomposition}
+\subsection{Updating Schemes}
+\subsection{Loop Updates}
 \begin{frame}{Quantum Monte Carlo}
 \begin{minipage}{0.45\linewidth}
 \begin{block}{XXZ Quantum Spin Chain}
@@ -322,6 +323,14 @@ Always accept the new configuration
 \end{block}
 \end{minipage}
 \end{frame}
+\begin{frame}{Loop Updates}
+\begin{minipage}{0.48\linewidth}
+	\includegraphics[width=\linewidth]{graphmap.pdf}
+\end{minipage}
+\hfill
+\begin{minipage}{0.48\linewidth}
+\end{minipage}
+\end{frame}
 
 {
 	\nocite{*}
-- 
GitLab