diff --git a/Manuscript/EPAWTFT.tex b/Manuscript/EPAWTFT.tex index 8723ec9..ca52e7f 100644 --- a/Manuscript/EPAWTFT.tex +++ b/Manuscript/EPAWTFT.tex @@ -1216,6 +1216,15 @@ A $[d_A/d_B]$ Pad\'e approximant is defined as (with $b_0 = 1$), where the coefficients of the polynomials $A(\lambda)$ and $B(\lambda)$ are determined by collecting terms according to power of $\lambda$. Pad\'e approximants are extremely useful in many areas of physics and chemistry \cite{Loos_2013,Gluzman_2020} as they can model poles, which appears at the roots of the polynomial $B(\lambda)$. However, they are unable to model functions with square-root branch points, which are ubiquitous in the singularity structure of a typical perturbative treatment. +Figure \ref{fig:PadeRMP} illustrates the improvement brought by Pad\'e approximants as compared to the usual Taylor expansion in the case of the RMP series of the Hubbard dimer for $U/t = 4.5$. + +%%%%%%%%%%%%%%%%% +\begin{figure} + \includegraphics[width=\linewidth]{PadeRMP} + \caption{\label{fig:PadeRMP} + RMP ground-state energy as a function of $\lambda$ obtained with various approximations for $U/t = 4.5$.} +\end{figure} +%%%%%%%%%%%%%%%%% %==========================================% \subsection{Quadratic approximant} diff --git a/Manuscript/PadeRMP.pdf b/Manuscript/PadeRMP.pdf new file mode 100644 index 0000000..e90f635 Binary files /dev/null and b/Manuscript/PadeRMP.pdf differ