  Antiferromagnetism and $d$-wave superconductivity are the most important
competing ground-state phases of cuprate superconductors. Using cellular
dynamical mean-field theory (CDMFT) for the Hubbard model, we revisit the
question of the coexistence and competition of these phases in the one-band
Hubbard model with realistic band parameters and interaction strengths. With an
exact diagonalization solver, we improve on previous works with a more complete
bath parametrization which is carefully chosen to grant the maximal possible
freedom to the hybridization function for a given number of bath orbitals.
Compared with previous incomplete parametrizations, this general bath
parametrization shows that the range of microscopic coexistence of
superconductivity and antiferromagnetism is reduced for band parameters for
NCCO, and confined to electron-doping with parameters relevant for YBCO.
