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We discuss the coexistence of antiferromagnetism and d-wave superconductivitywithin the so-called statistically-consistent Gutzwiller approximation (SGA)applied to the t-J-U model. In this approach, the averages calculated in aself-consistent manner coincide with those determined variationally. Suchconsistency is not guaranteed within the standard renormalized mean fieldtheory. With the help of SGA, we show that for the typical value J/|t| = 1/3,coexistence of antiferromagnetism (AF) and superconductivity (SC) appears onlyfor U/|t| > 10.6 and in a very narrow range of doping (\delta < 0.006) in thevicinity of the Mott insulating state, in contrast to some previous reports. Inthe coexistent AF+SC phase, a staggered spin-triplet component of thesuperconducting gap appears also naturally; its value is very small.

d-wave superconductivity and its coexistence with antiferromagnetism in t-J-U model: Statistically consistent Gutzwiller approach