Done with IIF
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@ -503,7 +503,7 @@ the total spin operator $\hat{\mathcal{S}}^2$, leading to ``spin-contamination''
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\begin{figure}
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\includegraphics[width=\linewidth]{HF_real.pdf}
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\caption{\label{fig:HF_real}
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RHF and UHF energies as a function of the correlation strength $U/t$.
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RHF and UHF energies \titou{in the Hubbard dimer} as a function of the correlation strength $U/t$.
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The symmetry-broken UHF solution emerges at the coalescence point $U=2t$ (black dot), often known as the Coulson-Fischer point.}
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\end{figure}
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%%%%%%%%%%%%%%%%%
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@ -553,7 +553,7 @@ modelling the correct physics with the two electrons on opposite sites.
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\subcaption{\label{subfig:UHF_cplx_energy}}
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\end{subfigure}
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\caption{%
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(\subref{subfig:UHF_cplx_angle}) Real component of the UHF angle $\ta^{\text{UHF}}$ for $\lambda \in \bbC$.
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(\subref{subfig:UHF_cplx_angle}) Real component of the UHF angle $\ta^{\text{UHF}}$ for $\lambda \in \bbC$ \titou{in the Hubbard dimer for $U/t = ??$}.
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Symmetry-broken solutions correspond to individual sheets and become equivalent at
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the \textit{quasi}-EP $\lambda_{\text{c}}$ (black dot).
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The RHF solution is independent of $\lambda$, giving the constant plane at $\pi/2$.
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@ -629,7 +629,7 @@ In contrast, $U < 2t$ yields $\lambda_{\text{c}} > 1$ and corresponds to
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the regime where the HF ground state is correctly represented by symmetry-pure orbitals.
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% COMPLEX ADIABATIC CONNECTION
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We have recently shown that the complex scaled Fock operator Eq.~\eqref{eq:scaled_fock}
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We have recently shown that the complex scaled Fock operator \eqref{eq:scaled_fock}
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also allows states of different symmetries to be interconverted by following a well-defined
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contour in the complex $\lambda$-plane.\cite{Burton_2019}
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In particular, by slowly varying $\lambda$ in a similar (yet different) manner
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