Global Quantum Discord in Transverse‐Field Ising Models on N × N Square Lattices

Abstract

Global quantum discord (GQD) in two‐dimensional (2D) transverse‐field Ising models on N × N square lattices at zero temperature and finite temperatures are studied. First, the GQD defined on the reduced density matrix of a 2 × 2 sub‐square in the center of the N × N lattices, with is studied. It is found that shows little size dependence in the strong‐field and weak‐field limit, and presents dramatic size dependence in the middle‐field region. The results are explained by short‐range correlations in non‐critical regions and long‐range correlations in critical regions of the models, respectively. Then the scaling behavior of the GQD of the ground states for the entire N × N squares is studied. It is found that contains a 1D contribution (corresponding to the side length of the squares) and a 2D contribution (corresponding to the area of the squares). Furthermore, the effect of thermodynamic fluctuations on GQD by investigating the thermal‐state GQD is considered. In high‐temperature regions, GQD is always destroyed by thermodynamic fluctuations for any strength of the magnetic field. However, in low‐temperature regions, some thermal enhancement of GQD under weak fields and some thermal robustness of GQD under strong fields is observed. The results are explained by the low‐lying energy states and the energy gap of the models.