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We study the ground state quantum correlation of Ising model in a transversefield (ITF) by implementing the quantum renormalization group (QRG) theory. Itis shown that various quantum correlation measures and theClauser-Horne-Shimony-Holt inequality will highlight the critical point relatedwith quantum phase transitions, and demonstrate nonanalytic phenomena andscaling behavior when the size of the systems becomes large. Our results alsoindicate a universal behavior of the critical exponent of ITF under QRG theorythat the critical exponent of different measures is identical, even when thequantities vary from entanglement measures to quantum correlation measures.This means that the two kinds of quantum correlation criterion including theentanglement-separability paradigm and the information-theoretic paradigm havesome connections between them. These remarkable behaviors may have importantimplications on condensed matter physics because the critical exponent directlyassociates with the correlation length exponent.

Universal quantum correlation close to quantum critical phenomena