Monogamy quantum correlation near the quantum phase transitions in the two-dimensional XY spin systems**Project supported by the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20171397), the National Natural Science Foundation of China (Grant Nos. 11535004, 11375086, 1175085, and 11120101005), the Foundation for Encouragement of College of Sciences (Grant No. LYLZJJ1616), and the Pre-research Foundation of Army Engineering University

Abstract

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.