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 λc, the hierarchy of the multipartite nonlocality increases dramatically,...
