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The purpose of the paper is mainly to investigate the quantum criticalbehavior of two-dimensional XY spin system by calculating quantum correlationand monogamy relation through implementation of quantum renormalization grouptheory. Numerical analysis indicates that quantum correlation as well asquantum nonlocality can be used to efficiently detect the quantum criticalproperty in two-dimensional XY spin system. The nonanalytic behavior of thefirst derivative of quantum correlation approaches infinity and the criticalpoint is reached as the size of the model increases. Furthermore, we discussthe quantum correlation distribution in this model based on square ofconcurrence (SC) and square of quantum discord (SQD). The monogamous propertiesof SC and SQD are obtained for the present system. We finally reveal that themonogamy score can be used to capture the quantum critical point.

Scaling of quantum correlation and monogamy relation near a quantum phase transitions in two-dimensional XY spin system