The singularity of quantum correlation has been widely regarded as a valuable indicator for quantum phase transition (QPT) in low-dimensional quantum systems. In this paper, in a two-leg spin ladder with ring exchange, the critical points of the system cannot be detected by analyzing the singularity of the quantum discord (a kind of quantum correlation). Instead, the discord exhibits a novel odd-even effect in the symmetry-breaking (SB) regions, which can be used to detect the two critical points between the SB regions and the non-SB regions. The underlying mechanism of the odd-even effect is ...
