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We have investigated the quantum phase transitions in the ground states ofseveral critical systems, including transverse field Ising and XY models aswell as XY with multiple spin interactions, XXZ and the collective systemLipkin-Meshkov-Glick models, by using different quantumness measures, such asentanglement of formation, quantum discord, as well as its classicalcounterpart, measurement-induced disturbance and theClauser-Horne-Shimony-Holt-Bell function. Measurement-induced disturbance isfound to detect the first and second order phase transitions present in thesecritical systems, while, surprisingly, it is found to fail to signal theinfinite-order phase transition present in the XXZ model. Remarkably, theClauser-Horne-Shimony-Holt-Bell function is found to detect all the phasetransitions, even when quantum and classical correlations are zero for therelevant ground state.

Correlation and nonlocality measures as indicators of quantum phase transitions in several critical systems