diff --git a/Manuscript/EPAWTFT.tex b/Manuscript/EPAWTFT.tex index 9af5c45..27f0813 100644 --- a/Manuscript/EPAWTFT.tex +++ b/Manuscript/EPAWTFT.tex @@ -727,7 +727,14 @@ The UMP partitioning yield the following $\lambda$-dependent Hamiltonian: \end{equation} \end{widetext} A closed-form expression for the ground-state energy can be obtained but it is cumbersome, so we eschew reporting it. -The radius of convergence of the UMP series can obtained numerically as a function of $U/t$ and is depicted in \titou{Fig.~\ref{eq:UMP_rc}}. +The radius of convergence of the UMP series can obtained numerically as a function of $U/t$ and is depicted in Fig.~\ref{fig:RadConv}. + +\begin{figure} + \includegraphics[width=\linewidth]{RadConv} + \caption{ + Evolution of the radius of convergence $r_c$ associated with the RMP ground state (red), the UMP ground state (blue), and the UMP excited state (orange) as functions of the ration $U/t$. + \label{fig:RadConv}} +\end{figure} The convergence of the UMP as a function of the ratio $U/t$ is shown in Fig.~\ref{subfig:UMP_cvg} for two specific values: the first ($U = 3t$) is well within the RMP convergence region, while the second ($U = 7t$) falls outside. 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