Multipartite nonlocality and boundary conditions in one-dimensional spin chains

Zhao-Yu Sun, Mei Wang, Yu-Yin Wu, and Bin Guo
Phys. Rev. A 99, 042323 – Published 15 April 2019

Abstract

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 δSS 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 δSS does not vanish in the large-N limit. Instead, at zero temperature, with the increase of N, δSS 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 δSTST of finite-size chains at finite temperatures, and show that boundary effects survive in finite temperature regions.

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  • Received 31 December 2018
  • Revised 24 February 2019

DOI:https://doi.org/10.1103/PhysRevA.99.042323

©2019 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Zhao-Yu Sun1,*, Mei Wang1, Yu-Yin Wu1, and Bin Guo2

  • 1School of Electrical and Electronic Engineering, Wuhan Polytechnic University, Wuhan 430023, China
  • 2Department of Physics, Wuhan University of Technology, Wuhan 430070, China

  • *Corresponding author: sunzhaoyu2000@qq.com

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Issue

Vol. 99, Iss. 4 — April 2019

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