From 261c8b2eb2238c9ba05f52f784c9fd0af541cb50 Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Tue, 1 Dec 2020 16:10:41 +0100 Subject: [PATCH] Done with IIF --- Manuscript/EPAWTFT.tex | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/Manuscript/EPAWTFT.tex b/Manuscript/EPAWTFT.tex index 15fffee..89fb780 100644 --- a/Manuscript/EPAWTFT.tex +++ b/Manuscript/EPAWTFT.tex @@ -503,7 +503,7 @@ the total spin operator $\hat{\mathcal{S}}^2$, leading to ``spin-contamination'' \begin{figure} \includegraphics[width=\linewidth]{HF_real.pdf} \caption{\label{fig:HF_real} - RHF and UHF energies as a function of the correlation strength $U/t$. + RHF and UHF energies \titou{in the Hubbard dimer} as a function of the correlation strength $U/t$. The symmetry-broken UHF solution emerges at the coalescence point $U=2t$ (black dot), often known as the Coulson-Fischer point.} \end{figure} %%%%%%%%%%%%%%%%% @@ -553,7 +553,7 @@ modelling the correct physics with the two electrons on opposite sites. \subcaption{\label{subfig:UHF_cplx_energy}} \end{subfigure} \caption{% - (\subref{subfig:UHF_cplx_angle}) Real component of the UHF angle $\ta^{\text{UHF}}$ for $\lambda \in \bbC$. + (\subref{subfig:UHF_cplx_angle}) Real component of the UHF angle $\ta^{\text{UHF}}$ for $\lambda \in \bbC$ \titou{in the Hubbard dimer for $U/t = ??$}. Symmetry-broken solutions correspond to individual sheets and become equivalent at the \textit{quasi}-EP $\lambda_{\text{c}}$ (black dot). The RHF solution is independent of $\lambda$, giving the constant plane at $\pi/2$. @@ -629,7 +629,7 @@ In contrast, $U < 2t$ yields $\lambda_{\text{c}} > 1$ and corresponds to the regime where the HF ground state is correctly represented by symmetry-pure orbitals. % COMPLEX ADIABATIC CONNECTION -We have recently shown that the complex scaled Fock operator Eq.~\eqref{eq:scaled_fock} +We have recently shown that the complex scaled Fock operator \eqref{eq:scaled_fock} also allows states of different symmetries to be interconverted by following a well-defined contour in the complex $\lambda$-plane.\cite{Burton_2019} In particular, by slowly varying $\lambda$ in a similar (yet different) manner