Regular Article

Multipartite quantum nonlocality in two-dimensional transverse-field Ising models on N × N square lattices

School of Electrical and Electronic Engineering, Wuhan Polytechnic University, Wuhan 430000, P.R. China

^a e-mail: sunzhaoyu2000@qq.com

Received: 20 October 2018
Received in final form: 12 February 2019
Published online: 8 April 2019

Abstract

We propose a procedure to transform two-dimensional (2D) tensor network states into one-dimensional (1D) tensor network states. With the help of the technique, we are able to investigate multipartite quantum nonlocality (characterized by Bell-type inequalities and Bell correlation function) of the ground states of 2D transverse-field Ising models on N × N square lattices. We find that in the thermodynamic limit, in a quite narrow region near the critical field λ_c, the hierarchy of the multipartite nonlocality increases dramatically, and the ground state transmutes into a highly correlated state. Furthermore, we study quantum correlations of several typical subregions on the square lattices, and disclose some direct numerical evidences for the competition between (1) the entanglement entropy which a subregion shares with its environment block and (2) the multipartite nonlocality which reserves in the subregion.