Integrable fermion model with hopping integrals for many particle configurations

One parametric one-dimensional spinless fermion models is formulated and solved exactly by the Bethe ansatz method. The Hamiltonian contains the kinetic terms describing nearest-neighbor hopping of electrons with different hopping integrals for many particle configurations. The Luttinger liquid behavior is studied for the case repulsion effective interactions. The ground state energy, the critical exponent, describing the asymptotic behavior of the density-density correlation function at long distances, the Fermi velocity have been calculated numerically for an arbitrary density of electrons. The model displays the condensation of particles in the case of the attractive interaction