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Temperature-dependent gap equations in the SU(4) model of high-Tcsuperconductivity are derived and analytical solutions are obtained. Based onthese solutions, a generic gap diagram describing the features of energy gapsas functions of doping P is presented and a phase diagram illustrating thephase structure as a function of temperature T and doping P is sketched. Aspecial doping point P_q occurs naturally in the solutions that separates twophases at temperature T = 0: a pure superconducting phase on one side (P > P_q)and a phase with superconductivity strongly suppressed by antiferromagnetism onthe 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 smallgap that is associated with competition between superconductivity andantiferromagnetism and is responsible for the ground state superconductivity,and a large gap without antiferromagnetic suppression that corresponds to acollective excited state. A pseudogap appears in the solutions that terminatesat P_q and originates from the competition between d-wave superconductivity andantiferromagnetism. Nevertheless, this conclusion does not contradict thepreformed pair picture conceptually if the preformed pairs are generallydefined as any pairs formed before pairing condensation.Comment: 23 pages, 5 color figure

Temperature-dependent gap equations and their solutions in the SU(4) model of high-temperature superconductivity