Multipartite quantum nonlocality and Bell-type inequalities in an infinite-order quantum phase transition of the one-dimensional spin-1/2 XXZ chain

摘要

In this paper, using the infinite time-evolving block decimation (iTEBD) algorithm and Bell-type inequalities, we investigate multipartite quantum nonlocality in an infinite one-dimensional quantum spin-1/2 XXZ system. High hierarchy of multipartite nonlocality can be observed in the gapless phase of the model, while only the lowest hierarchy of multipartite nonlocality is observed in most regions of the gapped antiferromagnetic phase. Thereby, Bell-type inequalities disclose different correlation structures in the two phases of the system. Furthermore, at the infinite-order quantum phase transition (QPT, or Kosterlitz-Thouless QPT) point of the model, the correlation measures always show a local minimum value, regardless of the length of the subchains. It indicates that relatively low hierarchy of multipartite nonlocality would be observed at the infinite-order QPT point in a Bell-type experiment. The result is in contrast to the existing results of the second-order QPT in the one-dimensional XY model, where multipartite nonlocality with the highest hierarchy has been observed. Thus, multipartite nonlocality provides an alternative perspective to distinguish between these two kinds of QPTs. Reliable clues for the existence of tripartite quantum entanglement have also been found.