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The intimate connection between antiferromagnetism and superconductivity isat the core of high-temperature superconductivity. Here, we put forward theprojected BCS theory for the unification of antiferromagnetism at half fillingand strongly correlated superconductivity at moderate doping. Specifically, itis shown that the projected BCS theory provides excellent trial states for theexact ground states of the $t$-$J$ model in the square lattice, generating theunified phase diagram as a continuous function of hole concentration. Preciselycapturing antiferromagnetism at half filling, which is ultimately a consequenceof the strong correlation between Cooper pairs, the projected BCS theory isable to produce better trial states for strongly correlated superconductivityat moderate doping than the resonating valence bond state. Finally, we discussvarious ramifications of the projected BCS theory.

Projected BCS Theory for the Unification of Antiferromagnetism and Strongly Correlated Superconductivity