  We discuss a cluster-like 1D system with triplet interaction. We study the
topological properties of this system. We find that the degeneracy depends on
the topology of the system, and well protected against external local
perturbations. All these facts show that the system is topologically ordered.
We also find a string order parameter to characterize the quantum phase
transition. Besides, we investigate two-site correlations including
entanglement, quantum discord and mutual information. We study the different
divergency behaviour of the correlations. The quantum correlation decays
exponentially in both topological and magnetic phases, and diverges in reversed
power law at the critical point. And we find that in TQPT systems, the global
difference of topology induced by dimension can be reflected in local quantum
correlations.
