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diff --git a/src/qmc-loop-algorithm-report.tex b/src/qmc-loop-algorithm-report.tex
index cb05c504b0da948eab23618aaeb155888f5abf3a..9629c9fd3b6b2cdfe12cc3a9ca370c33d8d314ee 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{*}