Abstract
In the paper, we have researched the monogamy relation and the quantum phase transition (QPT) in the anisotropic spin XXZ model by exploiting the quantum renormalization group method. The results show that there exits QPT after several iterations of renormalization in the present system. And we can find out that the monogamy inequality of entanglement of formation (EOF) and entropy quantum discord develop two saturated values which associate with spin-liquid and Neel phases after several iterations of the renormalization. Furthermore, we can also find out that the renormalization of EOF and entropy quantum discord violate the monogamy property while the renormalized geometric quantum discord obeys it no matter whether the QPT iterations are carried out. As a byproduct, the nonanalytic phenomenon and scaling behavior of the spin system are analyzed in detail.
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