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The so-called minimal models of unconventional superconductivity are latticemodels of interacting electrons derived from materials in which electronpairing arises from purely repulsive interactions. Showing unambiguously that aminimal model actually can have a superconducting ground state remains achallenge at nonperturbative interactions. We make a significant step in thisdirection by computing ground states of the 2D \mbox{U-V} Hubbard model - theminimal model of the quasi-1D superconductors - by parallelized DMRG, whichallows for systematic control of any bias and that is sign-problem-free. Usingdistributed-memory supercomputers and leveraging the advantages of the\mbox{U-V} model, we can treat unprecedented sizes of 2D strips and extrapolatetheir spin gap both to zero approximation error and the thermodynamic limit.Our results for the spin gap are shown to be compatible with a spin excitationspectrum that is either fully gapped or has zeros only in discrete points, andconversely that a Fermi liquid or magnetically ordered ground state isincompatible with them. Coupled with the enhancement to short-rangecorrelations that we find exclusively in the $d_{xy}$ pairing-channel, thisallows us to build an indirect case for the ground state of this model havingsuperconducting order in the full 2D limit, and ruling out the other mainpossible phases, magnetic orders and Fermi liquids.

Understanding repulsively mediated superconductivity of correlated electrons via massively parallel DMRG