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We study the phase diagram at finite temperature of a system of Fermiparticles on the sites of the Bethe lattice with coordination number z andinteracting through onsite U and nearest-neighbor V interactions. This is aphysical realization of the extended Hubbard model in the atomic limit. Byusing the equations of motion method, we exactly solve the model. For anattractive intersite potential, we find, at half filling, a phase transitiontowards a broken particle-hole symmetry state. The critical temperature, as afunction of the relevant parameters, has a re-entrant behavior as alreadyobserved in the equivalent spin-1 Ising model on the Bethe lattice.

Exact solution of the extended Hubbard model in the atomic limit on the Bethe Lattice