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- 12 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 tran...
