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

TL;DR

This study explores multi-partite quantum nonlocality in a 1D spin-1/2 XXZ chain using Bell inequalities and iTEBD, revealing distinct nonlocality hierarchies in different phases and at the infinite-order quantum phase transition.

Contribution

It demonstrates how Bell-type inequalities can distinguish between phases and quantum phase transitions in the XXZ model, highlighting the behavior of multi-partite nonlocality at the infinite-order transition.

Findings

High hierarchy of nonlocality in the gapless phase

Lowest hierarchy observed in most of the gapped phase

Local minimum of correlation measures at the infinite-order QPT

Abstract

In this paper, combined with infinite time-evolving block decimation (iTEBD) algorithm and Bell-type inequalities, we investigate multi-partite 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, meanwhile only the lowest hierarchy of multipartite nonlocality is observed in most regions of the gapped anti-ferromagnetic phase. Thereby, Bell-type inequalities disclose different correlation structures in the two phases of the system. Furthermore, at the infinite-order 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 multi-partite 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 multi-partite nonlocality with the hierarchy has been observed. Thus, multi-partite nonlocality provides us an alternative perspective to distinguish between these two kinds of QPTs. Reliable clues for the existence of tripartite quantum entanglement have also been found.