comment on Surjan section

This commit is contained in:
Pierre-Francois Loos 2020-12-03 16:30:16 +01:00
parent 4d305c9a50
commit 84f686863d

View File

@ -1730,7 +1730,7 @@ In a later study by the same group, they used analytic continuation techniques
to resum a divergent MP series such as a stretched water molecule.\cite{Mihalka_2017a}
Any MP series truncated at a given order $n$ can be used to define the scaled function
\begin{equation}
E_{\text{MP}n}(\lambda) = \sum_{k=0}^{n} \lambda^{k} E^{(k)}.
E_{\text{MP}n}(\lambda) = \sum_{k=0}^{n} \lambda^{k} \titou{E_\text{MP}^{(k)}}.
\end{equation}
Reliable estimates of the energy can be obtained for values of $\lambda$ where the MP series is rapidly
convergent (\ie, for $\abs{\lambda} < \rc$), as shown in Fig.~\ref{fig:rmp_anal_cont} for the RMP10 series
@ -1749,8 +1749,9 @@ It was then further improved by introducing Cauchy's integral formula\cite{Mihal
which states that the value of the energy can be computed at $\lambda_1$ inside the complex
contour $\mathcal{C}$ using only the values along the same contour.
Starting from a set of points in a ``trusted'' region where the MP series is convergent, their approach
self-consistently refines estimates of the $E(\lambda)$ values on a contour around the physical point
self-consistently refines estimates of the $E(\lambda)$ values on a contour \titou{around} the physical point
$\lambda = 1$.
\titou{T2: actually this is not true as the point $\lambda = 1$ is chosen to be on the contour.}
The shape of this contour is arbitrary, but there must be no branch points or other singularities inside
the contour.
Once the contour values of $E(\lambda)$ are converged, Cauchy's integral formula Eq.~\eqref{eq:Cauchy} can