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Pierre-Francois Loos 2020-12-01 15:56:04 +01:00
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Manuscript/EPAWTFT.tex
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@ -508,7 +508,7 @@ the total spin operator $\hat{\mathcal{S}}^2$, leading to ``spin-contamination''
\end{figure} \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} \begin{equation}
E_\text{HF}(\ta, \tb) = -t\, \qty( \sin \ta + \sin \tb ) + \frac{U}{2} \qty( 1 + \cos \ta \cos \tb ), E_\text{HF}(\ta, \tb) = -t\, \qty( \sin \ta + \sin \tb ) + \frac{U}{2} \qty( 1 + \cos \ta \cos \tb ),
\end{equation} \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} E_\text{RHF} \equiv E_\text{HF}(\ta^\text{RHF}, \tb^\text{RHF}) = -2t + \frac{U}{2}
\end{equation} \end{equation}
However, in the strongly correlated regime $U>2t$, the closed-shell orbital restriction prevents RHF from 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 (?) %%% %%% FIG 3 (?) %%%
% Analytic Continuation of HF % Analytic Continuation of HF