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Bell-CHSH function approach to quantum phase transitions in matrix product systems

Recently, nonlocality and Bell inequalities have been used to investigate quantum phase transitions (QPTs) in low-dimensional quantum systems. Nonlocality can be detected by the Bell-CHSH function (BCF). In this work, we extend the study of BCF to the QPTs in matrix product systems (MPSs). In this kind of QPTs, the ground-state energy keeps analytical in the vicinity of the QPT points, and is usually called the MPS-QPTs. For several typical models, our results show that BCF can signal the MPS-QPTs very well. In addition, we find BCF can capture signal of QPTs in unentangled states and classical states, for which other measures of quantum correlation (quantum entanglement and quantum discord) fail. Furthermore, we find that in these MPSs, there exists some kind of quantum correlation which cannot be characterized by entanglement, or by nonlocality.