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We investigate the role of quantum correlation around the quantum phase transitions by using quantum renormalization group theory.Numerical analysis indicates that quantum correlation as well as quantum nonlocality can efficiently detect the quantum critical point in the two-dimensional XY systems.The nonanalytic behavior of the first derivative of quantum correlation is observed at the critical point as the size of the model increases.Furthermore,we discuss the quantum correlation distribution in this system based on the square of concurrence (SC) and square of quantum discord (SQD).The monogamous properties of SC and SQD are obtained.Particularly,we prove that the quantum critical point can also be achieved by monogamy score.