Performance of various correlation measures in quantum renormalization-group method: A case study of quantum phase transition

Abstract

We have investigated quantum phase transition employing the quantum renormalization group (QRG) method while in most previous literature barely entanglement (concurrence) has been demonstrated. However, it is now well known that entanglement is not the only signature of quantum correlations and a variety of computable measures have been developed to characterize quantum correlations in the composite systems. As an illustration, two cases are elaborated: one dimensional anisotropic (i) XXZ model and (ii) XY model, with various measures of quantum correlations, including quantum discord (QD), geometric discord (GD), measure-induced disturbance (MID), measure-induced nonlocality (MIN) and violation of Bell inequalities (eg. CHSH inequality). We have proved that all these correlation measures can effectively detect the quantum critical points associated with quantum phase transitions (QPT) after several iterations of the renormalization in both cases. Nonetheless, it is shown that some of their dynamical behaviors are not totally similar with entanglement and even when concurrence vanishes there still exists some kind of quantum correlations which is not captured by entanglement. Intriguingly, CHSH inequality can never be violated in the whole iteration procedure, which indicates block-block entanglement can not revealed by the CHSH inequality. Moreover, the nonanalytic and scaling behaviors of Bell violation have also been discussed in detail. As a byproduct, we verify that measure-induced disturbance is exactly equal to the quantum discord measured by σ_z for general X-structured states.

Published version. 10 pages, 8 figures

References in corpus (8)

• Necessary and sufficient condition for non-zero quantum discord
• Quantum Phase Transitions and Bipartite Entanglement
• Quantum discord and quantum phase transition in spin chains
• Optimal measurements to access classical correlations of two-qubit states
• Phase Diagram and Entanglement of Ising Model With Dzyaloshinskii-Moriya Interaction
• Correlations in local measurements on a quantum state, and complementarity as an explanation of nonclassicality
• The renormalization of entanglement in the anisotropic Heisenberg (XXZ) model
• Phase Diagram of the One Dimensional $S=1/2$ $XXZ$ model with Ferromagnetic nearest-neighbor and Antiferromagnetic next-nearest neighbor interactions