Abstract
Here we employ trace distance and bipartite correlations as the detectors for quantum phase transitions (QPTs). Their performances behaving in Ising spin chains with Dzyaloshinskii–Moriya (DM) interaction and an external transverse field are studied, respectively. Exploiting the quantum renormalization group method, all the detectors can effectively characterize the QPTs at the critical points. Moreover, the block–block correlations existing in the multipartite spin systems never violate the Bell inequality with the DM interaction, whereas they are enough to violate this inequality under the transverse field. Finally, we detail the nonanalytic and scaling behavior of the trace distance, which is tightly connected to the critical features of spin systems.
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