Performance of various correlation measures in quantum phase transitions using the quantum renormalization-group method

摘要

We have investigated the quantum phase transition employing the quantum renormalization-group methodnwhile, in most of the previous literature, entanglement (concurrence) has been barely demonstrated. However,nit is now well known that entanglement is not the only signature of quantum correlations and a variety ofncomputable measures have been developed to characterize quantum correlations in the composite systems. As annillustration, two cases are elaborated: a one-dimensional anisotropic (i) XXZ model and (ii) an XY model, withnvarious measures of quantum correlations, including quantum discord, geometric discord, measurement-inducedndisturbance, measurement-induced nonlocality, and violation of Bell inequalities [e.g., Clauser-Horne-Shimony-nHolt (CHSH) inequality]. We have proved that all of these correlation measures can effectively detect thenquantum critical points associated with quantum phase transitions after several iterations of the renormalizationnin both cases. Nonetheless, it is shown that some of their dynamical behaviors are not totally similar withnentanglement and, even when concurrence vanishes, there still exists some kind of quantum correlation whichnis not captured by entanglement. Intriguingly, CHSH inequality can never be violated in the whole iterationnprocedure, which indicates that block-block entanglement cannot revealed by the CHSH inequality. Moreover,nthe nonanalytic and scaling behaviors of Bell violation have also been discussed in detail. As a by-product, wenverify that measurement-induced disturbance is exactly equal to the quantum discord measured by σz for generalnX-structured states.