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Hugh Burton 2020-12-02 20:34:29 +00:00
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@ -1669,7 +1669,10 @@ can significantly improve the estimate of the energy using low-order perturbatio
as shown in Table~\ref{tab:RMP_shank}. as shown in Table~\ref{tab:RMP_shank}.
Even though the RMP series diverges at $U/t = 4.5$, the combination Even though the RMP series diverges at $U/t = 4.5$, the combination
of diagonal Pad\'e approximants with the Shanks transformation reduces the absolute error of of diagonal Pad\'e approximants with the Shanks transformation reduces the absolute error of
the best energy estimate to 0.002\,\%.} the best energy estimate to 0.002\,\% using only the lowest 10 terms in the corresponding
Taylor series.}
This remarkable result indicates just how much information is contained in the first few
terms of a perturbation series, even if it diverges.
\begin{table}[th] \begin{table}[th]
\caption{ \caption{