Occupation-dependent virtual hopping
= Occupation-dependent virtual hopping
If site-transfer energies are $\mathcal E(\Delta)$, the left-ordered raising-hop generator has coefficient $f(\Delta)=t/[\mathcal E(\Delta)-\mathcal E(\Delta-2)]$. Nonlinear occupation energies generally make the effective second-order shifts and spin-exchange amplitudes depend on the occupation sector.