This is correct. The unperturbed hamiltonian has only the hubbard U interaction. So the eigenstates simply have some number of electrons on each site -- the ground state having a single electorn on each site, and excited states having some site vacant and other site double occupied.
THe perturbation moves (hops) electrons from one site to another. Any hopping takes you to an excited state from the ground state. In 2nd order you get back to the ground state again.
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