  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.
