Bosonic superexchange
= Bosonic superexchange
{title2=$J=-4t^2/U$}
Effective exchange of internal states through virtual <boson> hopping into energetically costly occupation sectors. For two <bosons> initially one per site and charging energy $U\Delta^2/4$, the second-order operator is $-(t^2/U)(3+4\mathbf s_a\cdot\mathbf s_b)$ for dimensionless <spins>. The triplet is lowered and the singlet is unchanged in this example; signs for other energy functions require their actual denominators.