Ferrimagnetism in the Hubbard, dimmer-connector frustrated chain

We study the AB2 "dimmer-connector" chain within a generalized Hubbard model, which contains site-dependent parameters, and different chemical potentials for A and B sites. Considering one electron per atom, we carry out exact calculations for finite clusters, and derive some asymptotic results, valid for macroscopic chains. We take a non-vanishing intra-dimmer electron hopping, thus departing from the condition of a bipartite lattice. In spite of that, the system persists ferrimagnetic in some region of the parameter space, thus generalizing a theorem of Lieb for bipartite lattices. A somewhat surprising result is that the ferrimagnetic phase is possible, even for a very large chemical potential jump between A and B sites. In another respect, we show that a previously reported macroscopic (2N) degenerancy of the AB2 Heisenberg chain ground state (GS) is fully removed on going to the (more fundamental) Hubbard model, yielding a non-magnetic GS.