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

TL;DR

This study evaluates various quantum correlation measures within the quantum renormalization group framework to detect quantum phase transitions, revealing that some measures outperform entanglement in identifying critical points.

Contribution

It introduces a comprehensive comparison of multiple quantum correlation measures in the QRG method, highlighting their effectiveness in detecting quantum criticality beyond entanglement.

Findings

All measures effectively detect quantum critical points.

Some quantum correlations persist even when entanglement vanishes.

CHSH inequality does not reveal block-block entanglement.

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 \sigma_z for general X-structured states.