磁学中纠缠在 Lindblad 或非马尔可夫动力学下的命运及其向 Landau-Lifshitz-Gilbert 经典动力学转变的条件
Fate of entanglement in magnetism under Lindbladian or non-Markovian dynamics and conditions for their transition to Landau-Lifshitz-Gilbert classical dynamics
AI总结：
该研究通过量子主方程模拟，发现非马尔可夫动力学保持纠缠阻碍 LLG 方程适用，而 Lindblad 动力学除小自旋反铁磁体外可实现量子到经典的转变，并考察了反铁磁纠缠基态的稳定性。
摘要：
在自旋电子学和磁子学中，通常假设反铁磁体中的局域自旋处于 Néel 基态（GS），并且当受到电流或外场驱动而偏离平衡时，该状态根据 Landau-Lifshitz-Gilbert (LLG) 方程演化，将局域自旋视为固定长度的经典矢量。另一方面，反铁磁体的真实基态是高度纠缠的，这一点已被最近的非弹性中子散射实验所证实。尽管铁磁体的基态总是非纠缠的，但其磁子低能激发是多体自旋态的叠加，因此是纠缠的。在本研究中，我们将量子 Heisenberg 铁磁或反铁磁链（包含局域自旋 $S=1/2$、$S=1$ 或 $S=5/2$）初始化为非纠缠纯态，然后通过 Lindblad 型或非马尔可夫型量子主方程（QME）对其进行演化，这些方程是通过将局域自旋耦合到玻色子浴（例如由声子引起的）或使用额外的“反应坐标”推导出来的。时间演化通过施加外部磁场来启动，并通过计算对数负性来监测时间演化的混合量子态的纠缠。我们发现，非马尔可夫动力学保持一定程度的纠缠，这会缩短自旋期望值矢量的长度，从而使 LLG 方程不适用。相反，Lindblad（即马尔可夫）动力学确保纠缠趋于零，从而在所有情况下——$S=1/2$、$S=1$ 和 $S=5/2$ 铁磁体或 $S=5/2$ 反铁磁体——实现量子到经典（即 LLG）的转变，除了 $S=1/2$ 和 $S=1$ 反铁磁体之外。我们还研究了纠缠的反铁磁基态在突然耦合到玻色子浴时的稳定性。
英文摘要：
It is commonly assumed in spintronics and magnonics that localized spins within antiferromagnets are in the Néel ground state (GS), as well as that such state evolves, when pushed out of equilibrium by current or external fields, according to the Landau-Lifshitz-Gilbert (LLG) equation viewing localized spins as classical vectors of fixed length. On the other hand, the true GS of antiferromagnets is highly entangled, as confirmed by very recent neutron scattering experiments witnessing their entanglement. Although GS of ferromagnets is always unentangled, their magnonic low-energy excitation are superpositions of many-body spin states and, therefore, entangled. In this study, we initialize quantum Heisenberg ferro- or antiferromagnetic chains hosing localized spins $S=1/2$, $S=1$ or $S=5/2$ into unentangled pure state and then evolve them by quantum master equations (QMEs) of Lindblad or non-Markovian type, derived by coupling localized spins to a bosonic bath (such as due to phonons) or by using additional ``reaction coordinate'' in the latter case. The time evolution is initiated by applying an external magnetic field, and entanglement of time-evolving {\em mixed} quantum states is monitored by computing its logarithmic negativity. We find that non-Markovian dynamics maintains some degree of entanglement, which shrinks the length of the vector of spin expectation values, thereby making the LLG equation inapplicable. Conversely, Lindbladian (i.e., Markovian) dynamics ensures that entanglement goes to zero, thereby enabling quantum-to-classical (i.e., to LLG) transition in all cases -- $S=1/2$, $S=1$ and $S=5/2$ ferromagnet or $S=5/2$ antiferromagnet -- {\em except} for $S=1/2$ and $S=1$ antiferromagnet. We also investigate the stability of entangled antiferromagnetic GS upon suddenly coupling it to the bosonic bath.
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