The behavior of the uncertainty relations and their tightness for a system, consisting of two qubits interacting thermally with a magnetic field in the presence of Dzyaloshinskii–Moriya interaction, is discussed, where different types of interaction strengths are considered. It is shown that both coupling and the magnetic field parameters decay the degree of entanglement, and increasing the uncertainty relations and the degree of mixedness. The phenomena of the sudden changes in the investigated quantities are depicted at large values of the field and coupling parameters. Concerning the type of the coupling parameters, distance and the trigonometric coupling have a clear effect on the behavior of the studied physical quantities.

中文翻译：

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具有长程相互作用的自旋 XY 模型中的熵不确定性

讨论了系统的不确定性关系及其紧密性的行为，该系统由两个量子位在存在 Dzyaloshinskii-Moriya 相互作用的情况下与磁场发生热相互作用，讨论了不同类型的相互作用强度。结果表明，耦合和磁场参数均会降低纠缠度，增加不确定性关系和混合度。在场和耦合参数的大值下描述了所研究量的突然变化现象。关于耦合参数的类型，距离和三角耦合对所研究的物理量的行为有明显的影响。