Correlation and nonlocality measures as indicators of quantum phase transitions in several critical systems
arXiv:1202.1495 · doi:10.1016/j.aop.2012.09.004
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.
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- Quantum discord and its allies: a review
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- Factorization and Criticality in the Anisotropic XY Chain via Correlations
- Nonviolation of Bell's Inequality in Translation Invariant Systems
- Multi-partite quantum nonlocality and Bell-type inequalities in an infinite-order quantum phase transition of the one-dimensional spin-1/2 XXZ chain
- Violation of Bell inequality in perfect translation invariant systems
- Enhancing the geometric quantum discord in the Heisenberg {\it XX} chain by Dzyaloshinsky-Moriya interaction
- Quantum uncertainty in critical systems with three spins interaction
- Bell-CHSH function approach to quantum phase transitions in matrix product systems
- Cumulative measure of correlation for multipartite quantum states
- Study of quantum non-locality by CHSH function and its extension in disordered fermions
- Bell Non-Locality in Many Body Quantum Systems with Exponential Decay of Correlations