Incommensurate and superconducting phases in an exactly solvable model

An integrable lattice model of strongly interacted electrons with nearest-neighbor and next-nearest-neighbor hoppings is proposed and investigated. The exact ground-state phase diagram is calculated as a function of an on-site interaction, a value of the hopping integral between next-nearest-neighbor lattice sites and a band filling (the nearest-neighbor hopping integral is chosen equal to unity). The model describes incommensurate and superconducting phases which are realized simultaneously in a definite region of interaction parameters and a band filling. The long-distance asymptotics of the density-density and one- particle correlation functions are calculated in the incommensurate phase