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.
We present an infinite-dimensional lattice of two-by-two plaquettes, the quadruple Bethe lattice, with Hubbard interaction and solve it exactly by means of the cluster dynamical mean-field theory. It exhibits a
d-wave superconducting phase that is related to a highly degenerate point in the phase diagram of the isolated plaquette at that the ground states of the particle number sectors
N=2,3,and4 cross. The superconducting gap is formed by the renormalized lower Slater peak of the correlated, hole-doped Mott insulator. We engineer parts of the interaction and find that pair hoppings between
X/Y momenta are the main two-particle correlations of the superconducting phase. The suppression of the superconductivity is caused by the diminishing of pair hopping correlations in the overdoped regime and by the charge blocking in the underdoped one. The optimal doping is $\ensuremath{\sim}0.15$ at which the underlying normal state shows a Lifshitz transition. Tuning intra- and interplaquette hoppings allows to disentangle superconductivity from antiferromagnetism as the latter requires larger interplaquette hoppings. We expect our results to provide additional insight into the nature of the superconductivity in cuprates.