The singularity of quantum correlations, such as quantum entanglement(QE) and quantum discord(QD), has been widely regarded as a valuable indicator for quantum phase transition(QPT) in low-dimensional quantum systems. In this paper, for a spin ladder system with ring exchange, we find that the singularity of QD (or QE) could not indicate the critical points of the system. Instead, the QD shows a novel odd-even effect in some phases, which can be used to detect the phase boundary points. The size effect is related to the symmetry breaking of the ladder.
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