Double occupancy of the Hubbard dimer
= Double occupancy of the Hubbard dimer
{title2=$P_{\rm double}=\tfrac12(1-U/\sqrt{U^2+16t^2})$}
The ground-state <probability> of both <electrons> occupying one site is $P_{\rm double}=\tfrac12[1-U/\sqrt{U^2+16t^2}]$. It equals the derivative of the relative ground energy with respect to $U$. It tends to zero for $|t|/U\to0$ and to $1/2$ for $|t|/U\to\infty$.