Global multipartite nonlocality and Bell-type inequalities in infinite-size quantum spin chains

Abstract

In this paper, we characterize the global multipartite nonlocality in one-dimensional infinite-size spin-1/2 chains. For this purpose, we calculate the multipartite nonlocality of $n$-site subchains, and take the large-$n$ limit. As $n$ increases from 2 to 100, we find that the average revenue and the marginal revenue of nonlocality converge gradually, thus they can be used to characterize the global multipartite nonlocality in infinite-size chains. Furthermore, in the vicinity of the quantum phase transition (QPT) points of the transverse-field Ising model and the $\mathit{XXZ}$ model, in the large-$n$ limit, multipartite nonlocality becomes extremely sensitive to external perturbation, that is, arbitrarily small perturbation away from the QPT points would lead to a drastic change in the global nonlocality. This signal of QPTs is easily distinguishable, and can be used to detect QPTs. We also draw a vivid physical picture of multipartite correlations and QPTs by analogy with magnetic domains in ferromagnets.