Multipartite nonlocality and boundary conditions in one-dimensional spin chains

报告题目:Multipartite nonlocality and boundary conditions in one-dimensional spin chains

报告人:孙照宇副教授 (武汉轻工大学电气学院)




报告摘要:In quantum lattice models, in the large-N 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 δS/S to characterize the boundary effects, where S is a measure of global multipartite nonlocality of the entire lattice, and δS is the difference of the measure induced by changing the boundary conditions. We find δS/S does not vanish in the large-N limit. Instead, at zero temperature, with the increase of N, δS/S 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 δST/ST of finite-size chains at finite temperatures, and show that boundary effects survive in finite temperature regions.