  The so-called minimal models of unconventional superconductivity are lattice
models of interacting electrons derived from materials in which electron
pairing arises from purely repulsive interactions. Showing unambiguously that a
minimal model actually can have a superconducting ground state remains a
challenge at nonperturbative interactions. We make a significant step in this
direction by computing ground states of the 2D \mbox{U-V} Hubbard model - the
minimal model of the quasi-1D superconductors - by parallelized DMRG, which
allows for systematic control of any bias and that is sign-problem-free. Using
distributed-memory supercomputers and leveraging the advantages of the
\mbox{U-V} model, we can treat unprecedented sizes of 2D strips and extrapolate
their 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 excitation
spectrum that is either fully gapped or has zeros only in discrete points, and
conversely that a Fermi liquid or magnetically ordered ground state is
incompatible with them. Coupled with the enhancement to short-range
correlations that we find exclusively in the $d_{xy}$ pairing-channel, this
allows us to build an indirect case for the ground state of this model having
superconducting order in the full 2D limit, and ruling out the other main
possible phases, magnetic orders and Fermi liquids.
