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Pierre-Francois Loos 2020-11-26 11:33:25 +01:00
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@ -1250,7 +1250,7 @@ More specifically, 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,Pavlyukh_2017,Tarantino_2019,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 $U/t = 4.5$.
Figure \ref{fig:PadeRMP} illustrates the improvement brought by diagonal (\ie, $d_A = d_B$) Pad\'e approximants as compared to the usual Taylor expansion in the case of the RMP series of the Hubbard dimer for $U/t = 4.5$.
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\begin{figure}