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

We have investigated the quantum phase transitions in the ground states of several critical systems, including transverse field Ising and XY models as well as XY with multiple spin interactions, XXZ and the collective system Lipkin–Meshkov–Glick models, by using different quantumness measures, such as entanglement of formation, quantum discord, as well as its classical counterpart, measurement-induced disturbance and the Clauser–Horne–Shimony–Holt–Bell function. Measurement-induced disturbance is found to detect the first and second order phase transitions present in these critical systems, while, surprisingly, it is found to fail to signal the infinite-order phase transition present in the XXZ model. Remarkably, the Clauser–Horne–Shimony–Holt–Bell function is found to detect all the phase transitions, even when quantum and classical correlations are zero for the relevant ground state.

► The ability of correlation measures to detect quantum phase transitions has been studied.
► Measurement induced disturbance fails to detect the infinite order phase transition.
► CHSH–Bell function detects all phase transitions even when the bipartite density matrix is uncorrelated.