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Re-added contour to fig1b

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Hugh Burton 2020-12-04 16:15:43 +00:00
parent f94b1d5470
commit b696acf6da
2 changed files with 1 additions and 2 deletions
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Manuscript/EPAWTFT.tex
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@ -338,7 +338,6 @@ unless otherwise stated, atomic units will be used throughout.
Exact energies for the Hubbard dimer ($U=4t$) as functions of $\lambda$ on the real axis (\subref{subfig:FCI_real}) and in the complex plane (\subref{subfig:FCI_cplx}). Exact energies for the Hubbard dimer ($U=4t$) as functions of $\lambda$ on the real axis (\subref{subfig:FCI_real}) and in the complex plane (\subref{subfig:FCI_cplx}).
Only the interacting closed-shell singlets are plotted in the complex plane, becoming degenerate at the EP (black dot). Only the interacting closed-shell singlets are plotted in the complex plane, becoming degenerate at the EP (black dot).
The contour followed around the EP in order to interchange states is also represented. The contour followed around the EP in order to interchange states is also represented.
\hugh{HUGH TO ADD CONTOUR AGAIN....}
\label{fig:FCI}} \label{fig:FCI}}
\end{figure*} \end{figure*}
@ -1927,7 +1926,7 @@ and applications of perturbation theory.
% DIRECTIONS % DIRECTIONS
Perturbation theory isn't usually considered in the complex plane. Perturbation theory isn't usually considered in the complex plane.
But when it is, we have seen that a lot can be learnt about the performance of perturbation theory on the real axis. But when it is, a lot can be learnt about the performance of perturbation theory on the real axis.
These insights can allow incredibly accurate results to be obtained using only the lowest-order terms in a perturbation series. These insights can allow incredibly accurate results to be obtained using only the lowest-order terms in a perturbation series.
Yet perturbation theory represents only one method for approximating the exact energy, and few other methods Yet perturbation theory represents only one method for approximating the exact energy, and few other methods
have been considered through similar complex non-Hermitian extensions. have been considered through similar complex non-Hermitian extensions.

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Manuscript/fig1b.pdf
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