Abstract
In quantum lattice models, in the large- limit, boundary conditions have little effect upon local observables for sites in the centers of the lattices. In this paper, we will study the boundary effects upon multipartite nonlocality (a kind of multipartite quantum correlation associated with Bell-type inequalities) in one-dimensional finite-size spin chains, both for zero temperature and for finite temperatures. We define a quantity to characterize the boundary effects, where is a measure of global multipartite nonlocality of the entire lattice, and is the difference of the measure induced by changing the boundary conditions. We find does not vanish in the large- limit. Instead, at zero temperature, with the increase of , would increase steadily in the vicinity of the quantum phase transition point of the models, and converge to a nonzero constant in noncritical regions. It shows clearly that boundary effects generally exist, in the form of multipartite correlations, in long chains. The boundary effects are explained by the competition between the two orders of the models. In addition, based on these numerical results, we construct a Bell inequality, which is violated by chains with periodic (closed) boundary conditions and not violated by chains with open boundary conditions. Furthermore, we study of finite-size chains at finite temperatures, and show that boundary effects survive in finite temperature regions.
3 More- Received 31 December 2018
- Revised 24 February 2019
DOI:https://doi.org/10.1103/PhysRevA.99.042323
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