 Virtual hopping

A hopping process through an intermediate configuration of different unperturbed energy, contributing to a low-energy effective description through perturbation theory. If an intermediate state costs $\Delta >0$, second-order nondegenerate perturbation theory gives a contribution $-|⟨a|T|0⟩{|}^2/\Delta$. Its amplitude is of order $t/\Delta$ and its energy correction of order $-t^2/\Delta$; a degenerate low-energy sector requires the corresponding degenerate perturbation theory before identifying the ground state.