Monogamy quantum deficit in the one-dimensional Heisenberg XY model

Monogamy relation of quantum correlations have many potential applications in quantum information processing. However, our understandings about using monogamy relation of quantum correlation to investigate quantum phase transitions are still very limited. In this paper, we study the quantum correlation based on the quantum deficit in the one-dimensional XY model by employing quantum renormalization group theory. We show that the first derivative of quantum deficit will develop two peak values after enough times iterations. The scaling behavior is manifested through increase the size of the systems. Monogamy relation is formulated for this model and the result show that it is suitable to detect the quantum critical point.