Characterization Of Quantum Phase Transition In The Xy Model With Multipartite Correlations And Bell-Type Inequalities

The ground state of interacting spin chains in external magnetic fields can undergo a quantum phase transition (QPT) characterized by dramatic changes at a critical value of the magnetic field. In this paper, we use Bell-type inequalities to study the multipartite correlations (including multipartite entanglement and multipartite nonlocality in an n-spin subsystem) in the QPT of an infinite XY chain. An efficient numerical optimization procedure is proposed to figure out the violation measure M-n of the inequalities. For n <= 7, the magnetic-field (lambda) dependence of M-n is studied. We find the derivative of M-n is divergent exactly at the QPT point lambda(c) = 1 for any n. In addition, with the increase of n, M-n converges quickly for lambda < lambda(c) and converges very slowly for lambda > lambda(c), which can be regarded as another signal for the QPT. Furthermore, in the vicinity of lambda(c), high-order Bell-type inequalities will be violated as long as n is large enough. This indicates that high-level multipartite correlation will be present when the system is in the vicinity of the QPT point. Nevertheless, genuine n-partite entanglement or genuine n-partite nonlocality is not observed in the QPT.