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

Abstract

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

18 pages, 7 figures

References in corpus (8)

• Necessary and sufficient condition for non-zero quantum discord
• Diverging Entanglement Length in Gapped Quantum Spin Systems
• Monogamy Inequality in terms of Negativity for Three-Qubit States
• Phase Diagram and Entanglement of Ising Model With Dzyaloshinskii-Moriya Interaction
• The renormalization of entanglement in the anisotropic Heisenberg (XXZ) model
• Performance of various correlation measures in quantum renormalization-group method: A case study of quantum phase transition
• Berry phase and quantum criticality in Yang--Baxter systems
• Quantum renormalization group of XY model in two dimensions