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We present an infinite-dimensional lattice of two-by-two plaquettes, thequadruple Bethe lattice, with Hubbard interaction and solve it exactly by meansof the cluster dynamical mean-field theory. It exhibits a $d$-wavesuperconducting phase that is related to a highly degenerate point in the phasediagram of the isolated plaquette at that the groundstates of the particlenumber sectors $N=2,3,4$ cross. The superconducting gap is formed by therenormalized lower Slater peak of the correlated, hole-doped Mott insulator. Weengineer parts of the interaction and find that pair hoppings between$X/Y$-momenta are the main two-particle correlations of the superconductingphase. The suppression of the superconductivity in the overdoped regime iscaused by the diminishing of pair hopping correlations and in the underdopedregime by charge blocking. The optimal doping is $\sim 0.15$ at which theunderlying normal state shows a Lifshitz transition. The model allows fordifferent intra- and inter-plaquette hoppings that we use to disentanglesuperconductivity from antiferromagnetism as the latter requires largerinter-plaquette hoppings.

Exactly solvable model of strongly correlated $d$-wave superconductivity