Hamiltonian degenerate Hubbard

Now we generalize this density matrix formalism [19,20] for the degenerate Hubbard Hamiltonian which, with usual notations, reads ... 

For one hole in the half-filled band, the exact energy spectrum of the chain with free ends formed by L unit cells is spin-degenerate, similar to the spectrum of the uniform Hubbard chain with U = oo. In the case of periodic boundary conditions an electron hopping between the first and the last unit cells of the chain leads to the additional term to the Hamiltonian (9). For one hole in the half-filled band this term has the following form ... 

To cover the gap between them the Hubbard model Hamiltonian was quite generally accepted. This Hamiltonian apparently has the ability of mimicking the whole spectrum, from the free quasi-particle domain, at U=0, to the strongly correlated one, at U —> oo, where, for half-filled band systems, it renormalizes to the Heisenberg Hamiltonian, via Degenerate Perturbation Theory. Thence, the Heisenberg Hamiltonian was assumed to be acceptable only for rather small t/U values. 

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