  Extensive numerical studies have demonstrated that the two-dimensional
single-band Hubbard model contains much of the key physics in cuprate
high-temperature superconductors. However, there is no definitive proof that
the Hubbard model truly possesses a superconducting ground state or, if it
does, of how it depends on model parameters. To answer these longstanding
questions, we study an extension of the Hubbard model including an
infinite-range d-wave pair field term, which precipitates a superconducting
state in the d-wave channel. Using exact diagonalization on 16-site square
clusters, we study the evolution of the ground state as a function of the
strength of the pairing term. This is achieved by monitoring the fidelity
metric of the ground state, as well as determining the ratio between the two
largest eigenvalues of the d-wave pair/spin/charge-density matrices. The
calculations show a d-wave superconducting ground state in doped clusters
bracketed by a strong antiferromagnetic state at half filling controlled by the
Coulomb repulsion U and a weak short-range checkerboard charge ordered state at
larger hole doping controlled by the next-nearest-neighbor hopping t'. We also
demonstrate that negative t' plays an important role in facilitating d-wave
superconductivity.
