Two Neighbor Segments with Different Filling

For simplicity, let us first consider the case of two-site segments with 3 electrons and t3=0. Because of infinite electron repulsion there are only two 

The Hamiltonian (8) can also be rewritten in a pure spin form if the spin space of double dimensionality is taken into account 

For t3 0 the Hamiltonian describing the interaction of two neighbor two-site segments with one and two electrons has the form 

It is easily seen, that to change the numeration of electrons we can obtain similar Hamiltonian H with Hermitian matrix A  

This Hamiltonian has the same spectrum because of the identity 

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