  Temperature-dependent gap equations in the SU(4) model of high-Tc
superconductivity are derived and analytical solutions are obtained. Based on
these solutions, a generic gap diagram describing the features of energy gaps
as functions of doping P is presented and a phase diagram illustrating the
phase structure as a function of temperature T and doping P is sketched. A
special doping point P_q occurs naturally in the solutions that separates two
phases at temperature T = 0: a pure superconducting phase on one side (P > P_q)
and a phase with superconductivity strongly suppressed by antiferromagnetism on
the other (P < P_q). We interpret P_q as a quantum phase transition point.
Moreover, the pairing gap is found to have two solutions for P < P_q: a small
gap that is associated with competition between superconductivity and
antiferromagnetism and is responsible for the ground state superconductivity,
and a large gap without antiferromagnetic suppression that corresponds to a
collective excited state. A pseudogap appears in the solutions that terminates
at P_q and originates from the competition between d-wave superconductivity and
antiferromagnetism. Nevertheless, this conclusion does not contradict the
preformed pair picture conceptually if the preformed pairs are generally
defined as any pairs formed before pairing condensation.
