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Global Quantum Discord in Transverse‐Field Ising Models on N × N Square Lattices
Author(s) -
Sun ZhaoYu,
Zhou Mu,
Wang Mei,
Fu Jin
Publication year - 2019
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.201800666
Subject(s) - scaling , condensed matter physics , ising model , physics , ground state , square (algebra) , magnetic field , quantum mechanics , mathematics , geometry
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 G ( ρ 2 × 2 )defined on the reduced density matrixρ 2 × 2of a 2 × 2 sub‐square in the center of the N × N lattices, with N = 4 , 5 , 6 , 7 , ∞ is studied. It is found that G ( ρ 2 × 2 )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 G ( | ψ g 〉 )of the ground states for the entire N × N squares is studied. It is found that G ( | ψ g 〉 )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 G ( e − H k B T)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.