Re-added contour to fig1b
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@ -338,7 +338,6 @@ unless otherwise stated, atomic units will be used throughout.
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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}).
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Only the interacting closed-shell singlets are plotted in the complex plane, becoming degenerate at the EP (black dot).
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The contour followed around the EP in order to interchange states is also represented.
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\hugh{HUGH TO ADD CONTOUR AGAIN....}
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\label{fig:FCI}}
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\end{figure*}
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@ -1927,7 +1926,7 @@ and applications of perturbation theory.
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% DIRECTIONS
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Perturbation theory isn't usually considered in the complex plane.
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But when it is, we have seen that a lot can be learnt about the performance of perturbation theory on the real axis.
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But when it is, a lot can be learnt about the performance of perturbation theory on the real axis.
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These insights can allow incredibly accurate results to be obtained using only the lowest-order terms in a perturbation series.
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Yet perturbation theory represents only one method for approximating the exact energy, and few other methods
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have been considered through similar complex non-Hermitian extensions.
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