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

Abstract

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.

Nonclassicality Indicators of Quantum Phase Transition in the XY Model with Dzyaloshinskii-Moriya Interaction

“…Evidently, it is demonstrated that the lack of any optimization procedure over the set of projective measurements in the definition of MID leads to a fact that MID can be non-full and even maximal on states exhibiting zero quantum correlations. Such many shortcomings make it a weak correlation measure for some states [21,[48][49][50]. Girolami et al [21] introduce an improved version of MID, i.e.…”

Nonviolation of Bell’s inequality in translation invariant systems

“…Indeed, different correlations may be associated with resources for distinct tasks. As for entanglement and discord, characterization of QPTs through Bell correlations between qubits through the Clauser-Horne-Shimony-Holt (CHSH) inequality has recently been addressed [14][15][16][17]. However, it is rather surprising that the CHSH inequality, when applied for any pair of qubits in critical spin latices, has been observed to be nonviolated in a number of different systems (see, e.g., Refs.…”

“…Very recently, the CHSH inequality has been used as a tool to characterize QPTs [14][15][16][17]. In turn, it has successfully performed this task, indicating QPTs through nonanalyticities in the derivatives of the Bell correlations.…”

Comparative study of the geometric quantum discord in the transverse Ising model

“…Recently, quantum discord in various spin models have been studied by a number of authors [46][47][48][49][50][51][52][53][54][55][56]. Particularly, the spin-1/2 model with Ising interactions between neighbors has attracted wide attention due to its clear physical picture.…”