From 3b734bb96dbe8c37e41d58e44fb3667b9759e851 Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Tue, 1 Dec 2020 15:56:04 +0100 Subject: [PATCH] Done with IIE --- Manuscript/EPAWTFT.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/Manuscript/EPAWTFT.tex b/Manuscript/EPAWTFT.tex index e792b59..15fffee 100644 --- a/Manuscript/EPAWTFT.tex +++ b/Manuscript/EPAWTFT.tex @@ -508,7 +508,7 @@ the total spin operator $\hat{\mathcal{S}}^2$, leading to ``spin-contamination'' \end{figure} %%%%%%%%%%%%%%%%% -In the Hubbard dimer, the UHF energy can be parametrised using two rotation angles $\ta$ and $\tb$ as +In the Hubbard dimer, the HF energy can be parametrised using two rotation angles $\ta$ and $\tb$ as \begin{equation} E_\text{HF}(\ta, \tb) = -t\, \qty( \sin \ta + \sin \tb ) + \frac{U}{2} \qty( 1 + \cos \ta \cos \tb ), \end{equation} @@ -538,7 +538,7 @@ and the ground-state RHF energy (Fig.~\ref{fig:HF_real}) E_\text{RHF} \equiv E_\text{HF}(\ta^\text{RHF}, \tb^\text{RHF}) = -2t + \frac{U}{2} \end{equation} However, in the strongly correlated regime $U>2t$, the closed-shell orbital restriction prevents RHF from -modelling the correct physics with the two electrons on opposing sites. +modelling the correct physics with the two electrons on opposite sites. %%% FIG 3 (?) %%% % Analytic Continuation of HF