reviewing Hugh changes
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@ -1405,7 +1405,7 @@ This swapping process can also be represented as a double excitation, and thus a
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for $\lambda \geq 1$ (Fig.~\ref{subfig:ump_cp}).
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While this appears to be an avoided crossing between the ground and first-excited state,
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the presence of an earlier excited-state avoided crossing means that the first-excited state qualitatively
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represents the reference double excitation for $\lambda > 0.5.$
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represents the reference double excitation for $\lambda > 1/2$ (see Fig.~\ref{subfig:ump_cp}).
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% SHARPNESS AND QPT
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The ``sharpness'' of the avoided crossing is controlled by the correlation strength $U/t$.
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