more tweaks

Manuscript/EPAWTFT.tex

@@ -465,12 +465,16 @@ the total spin $\hat{\mathcal{S}}^2$ operator, leading to so-called ``spin-conta
 %Because $Y_0(\theta) = 1/\sqrt{4\pi}$, it is clear that the RHF wave function yields a uniform one-electron density.
 %
 
+%%% FIG 2 (?) %%%
+% HF energies as a function of U/t
+%%%%%%%%%%%%%%%%%
 \begin{figure}
-\includegraphics[width=\linewidth]{HF_real.pdf}
-\caption{\label{fig:HF_real}
-\hugh{RHF and UHF energies as a function of the correlation strength $U/t$. 
-The symmetry-broken UHF solution emerges at the coalescence point $U=2t$ (black dot).}}
+    \includegraphics[width=\linewidth]{HF_real.pdf}
+    \caption{\label{fig:HF_real}
+    \hugh{RHF and UHF energies as a function of the correlation strength $U/t$. 
+    The symmetry-broken UHF solution emerges at the coalescence point $U=2t$ (black dot).}}
 \end{figure}
+%%%%%%%%%%%%%%%%%
 
 Returning to the Hubbard dimer, the UHF energy can be parametrised in terms of two rotation angles $\ta$ and $\tb$ as
 \begin{equation}
@@ -515,7 +519,7 @@ correctly modelling the physics of the system with the two electrons on opposing
     \end{subfigure}
 	\caption{%
     \hugh{(\subref{subfig:UHF_cplx_angle}) Real component of the UHF angle $\ta^{\text{UHF}}$ for $\lambda \in \bbC$.
-    Symmetry-broken solutions correspond to an individual sheets and become equivalent at the quasi-EP (black dot).
+    Symmetry-broken solutions correspond to individual sheets and become equivalent at the quasi-EP $\lambda_{\text{c}}$ (black dot).
     The RHF solution is independent of $\lambda$, giving constant plane at $\pi/2$.
     (\subref{subfig:UHF_cplx_energy}) The corresponding HF energy surfaces show a non-analytic 
     point at the quasi-exceptional point.}