  Doped Hubbard model is a simple model for the high-Tc cuprate
superconductors, while its ground state remains a challenge. Here, by
performing state-of-the-art variational Monte Carlo calculations for the
strong-coupling Hubbard model, we find evidences that the d-wave
superconducting phase emerges always near the phase separation region and the
superconducting order has one-to-one correspondence with the enhancement of
charge compressibility. The order as well as the phase separation are
vulnerable to realistic intersite Coulomb interaction while the superexchange
interaction enhances both. An appropriate combination of these two widens the
stable superconducting phase.
