= Single-orbital interacting defect
= Interacting point defect
{synonym}
An isolated spin-degenerate orbital coupled to a particle reservoir has <Hamiltonian> $H=\epsilon(n_\uparrow+n_\downarrow)+Un_\uparrow n_\downarrow$. The four occupation <microstates> have weights $1,z,z,qz^2$, where $z=e^{\beta(\mu-\epsilon)}$ and $q=e^{-\beta U}$. Thus $\Xi=1+2z+qz^2$ and $\bar n=(2z+2qz^2)/\Xi$. The factor two counts distinct <spin> states. At $U=0$ the grand <partition function> factorizes into two <independent> fermionic orbitals; positive U separates the two electron-addition thresholds.
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