= Exchange interaction in a double quantum dot
{title2=$H_{\rm ex}=J\boldsymbol\sigma_1\cdot\boldsymbol\sigma_2/4$}
An effective coupling that separates the two-electron <singlet state> and <triplet states> by energy $J$. For a symmetric two-site Hubbard model with weak tunnelling $t_c$ and charging cost $U$, $J\simeq4t_c^2/U$. Gate-controlled detuning and tunnelling change the interaction; the simple expression does not hold at arbitrary detuning or strong charge hybridization.
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