Abstract
The problem of two electrons on a one-dimensional (1D) lattice is solved for the case when the lattice unit cell contains two unequivalent sites a and b with two corresponding electron-electron correlation potentials: attractive Ua and repulsive Ub. It is shown, that the kinematics of the electron-electron scattering in such a system are remarkably different from those of the ordinary 1D Hubbard model because of the presence of the Umklapp processes. Analytical properties of the S-matrix are studied. Ground state properties and excitation spectrum are analyzed as functions of Ua and Ub.
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