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We have studied the extended Hubbard model with pair hopping in the atomiclimit for arbitrary electron density and chemical potential. The Hamiltonianconsidered consists of (i) the effective on-site interaction U and (ii) theintersite charge exchange interactions I, determining the hopping of electronpairs between nearest-neighbour sites. The model can be treated as a simpleeffective model of a superconductor with very short coherence length in whichelectrons are localized and only electron pairs have possibility oftransferring. The phase diagrams and thermodynamic properties of this modelhave been determined within the variational approach, which treats the on-siteinteraction term exactly and the intersite interactions within the mean-fieldapproximation. We have also obtained rigorous results for a linear chain (d=1)in the ground state. Moreover, at T=0 some results derived within the randomphase approximation (and the spin-wave approximation) for d=2 and d=3 latticesand within the low density expansions for d=3 lattices are presented. Ourinvestigation of the general case (as a function of the electron concentrationand as a function of the chemical potential) shows that, depending on thevalues of interaction parameters, the system can exhibit not only thehomogeneous phases: superconducting (SS) and nonordered (NO), but also thephase separated states (PS: SS-NO). The system considered exhibits interestingmulticritical behaviour including tricritical points.

Phase separation in a lattice model of a superconductor with pair hopping