add example

src/qmc-loop-algorithm-report.tex

@@ -401,6 +401,34 @@ Always accept the new configuration
 \end{minipage}
 \blfootnote{\cite{Assaad}}
 \end{frame}
+\begin{frame}{Example}
+\begin{minipage}{0.48\linewidth}
+\begin{block}{Heisenberg Model}
+\begin{align*}
+	H = J\sum_i (S_i^xS_{i+1}^x + S_i^yS_{i+1}^y + S_i^zS_{i+1}^z)
+\end{align*}
+\(\implies\) Only graphs \(G=1\) and \(G=2\) need to be considered
+\end{block}
+\begin{block}{System of Equations}
+	\begin{align*}
+		e^{\Delta\tau J /4}\cosh(\Delta\tau J /2) &= W_1 = W_{1,1} + W_{1,2} \\
+		e^{\Delta\tau J /4}\sinh(\Delta\tau J /2) &= W_2 = W_{2,2} = W_{1,2} \\
+		e^{-\Delta\tau J /4} &= W_3 = W_{1,1} = W_{3,1}
+	.\end{align*}
+\end{block}
+\end{minipage}
+\hfill
+\begin{minipage}{0.48\linewidth}
+\begin{block}{Horizontal Breakup Probabilities}
+\begin{align*}
+	\vcenter{\hbox{\includegraphics{square.left.pdf}}}, \vcenter{\hbox{\includegraphics{square.right.pdf}}} &\equiv \tanh(\Delta\tau J /2) \\
+	\vcenter{\hbox{\includegraphics{square.diag.lr.pdf}}}, \vcenter{\hbox{\includegraphics{square.diag.rl.pdf}}} &\equiv 1 \\
+	\vcenter{\hbox{\includegraphics{square.none.pdf}}}, \vcenter{\hbox{\includegraphics{square.left.right.pdf}}} &\equiv 0
+.\end{align*}
+\end{block}
+\end{minipage}
+\blfootnote{Assaad}
+\end{frame}
 \subsection{Sign Problem}
 \begin{frame}{Sign Problem}
 \begin{minipage}{0.48\linewidth}