The two-dimensional extended Hubbard model that includes a nearest-nei
ghbor Heisenberg interaction is studied using a mean-held theory where
quasiparticles are defined by an U(8) group of canonical transformati
ons permitting both broken gauge, spin, and sublattice symmetry. The t
heory is further extended to incorporate a possible twist in the spin-
quantization axis, so that the competition between superconductivity,
charge-density waves, and Neel and spiral antiferromagnetic order can
be monitored within one single theory. Our results for positive Hubbar
d U and Heisenberg exchange J suggest that antiferromagnetic ordering
dominates close to half-filling, while spiral states and d-wave superc
onductivity compete when doping is introduced. For moderate values of
J, we find a phase diagram where a phase transition occurs from an ant
iferromagnet to a d-wave superconductor as doping is increased. A narr
ow region of (s + id)-wave superconductor is found for some values of
J and U.