Thermal quantum Fisher information and influence of magnetic field distribution in a two-qubit XXZ spin model

In this work, we investigate the quantum Fisher information (QFI) of a thermal two-qubit XXZ Heisenberg spin model. Here, we adopt the average QFI with respect to the local orthonormal observable bases (Li and Luo in Phys Rev A 88:014301, 2013). Meanwhile, the QFI is compared with two other quantum correlations (concurrence and trace distance discord). Their dependence on uniform magnetic field, non-uniform magnetic field, and coupling constant is calculated and discussed in details. Their evolution behaviors in terms of various model parameters are compared. The results show that at finite temperature, the concurrence is weaker, while QFI and trace distance discord is stronger. And even if the temperature is higher, QFI’s change with the magnetic field is still obvious, while the trace distance discord is almostly the same and indistinguishable under different fields. Particularly, it can be seen that QFI is asymmetric with respect to coupling strength zero based on which we can judge whether the system is ferromagnetic or antiferromagnetic. In addition, the modification effect of non-uniform field is more evident for the QFI. Finally, their thermal evolution behaviors are discussed, and quantum phase transition points can be rapidly derived from the evolutionary properties under uniform field. Our numerical results are well consistent with theoretical analysis. On the whole, it is demonstrated that the QFI should be a more effective order parameter of the studied spin system.