When can localized spins interacting with conduction electrons in ferro- or antiferromagnets be described classically via the Landau-Lifshitz equation: Transition from quantum many-body entangled to quantum-classical nonequilibrium states
When can localized spins interacting with conduction electrons in ferro- or antiferromagnets be described classically via the Landau-Lifshitz equation: Transition from quantum many-body entangled to quantum-classical nonequilibrium states
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DOI：
10.1103/physrevb.104.214401
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发表时间：
2021-12-02
影响因子：
3.7
通讯作者：
Nikolic, Branislav K.
中科院分区：
文献类型：
--
作者：
Mondal, Priyanka;Suresh, Abhin;Nikolic, Branislav K.
自旋电子学和磁振子学的实验在铁磁 (F) 或反铁磁 (AF) 材料中使用宏观上大量的局域自旋，因此它们的非平衡动力学标准地由 Landau-Lifshitz (LL) 方程描述，将局域自旋视为固定长度的经典向量。然而，自旋是真正的量子自由度，尽管量子效应对于自旋值 S 无穷大来说变得越来越不重要。虽然这激发了对 LL 方程的限制/分解的探索——通过使用 F 绝缘体的例子来比较 LL 轨迹与局域自旋算子的量子期望值——但在存在非平衡传导电子的系统中缺乏全量子多体与量子（对于电子）-经典（对于局域自旋）动力学的类似比较。在这里，我们采用 N = 4 个位点的量子海森堡 F 或 AF 链，其局域自旋通过 sd 交换相互作用与传导电子相互作用，以局域自旋的非纠缠纯（零温度）或混合（有限温度）量子态作为初始条件来进行这种比较。这表明量子经典动力学可以在 F 金属情况下忠实地再现完全量子动力学，但前提是自旋 S、局域自旋之间的海森堡交换和 sd 交换足够小。增加这三个参数中的任何一个都可能导致显着的偏差，这是通过局部自旋之间和/或它们与电子之间的纠缠的动态累积来解释的。在 AF 金属情况下，尽管是从非纠缠的尼尔态开始，但即使在早期也会出现很大的偏差，因此，这对如何严格证明 LL 方程在反铁磁自旋电子学实验唯象建模中的广泛使用提出了挑战。我们还讨论了有限温度和有限尺寸效应，以证明：（i）包括热波动会延迟纠缠动态积累的开始，但不会抑制它； (ii) 当我们将链长增加到 N 4 位点时，这个特定问题的动力学不会发生显着变化，而即使 N = 4 也足以观察量子混沌能级统计，其在如此小的量子多体系统中的出现关键依赖于局域自旋和传导电子之间的相互作用。
Experiments in spintronics and magnonics operate with a macroscopically large number of localized spins within ferromagnetic (F) or antiferromagnetic (AF) materials, so that their nonequilibrium dynamics is standardly described by the Landau-Lifshitz (LL) equation treating localized spins as classical vectors of fixed length. However, spin is a genuine quantum degree of freedom, and even though quantum effects become progressively less important for spin value S infinity. While this has motivated exploration of limitations/breakdown of the LL equation-by using examples of F insulators to compare LL trajectories with quantum expectation values of localized spin operators-analogous comparison of fully quantum many-body vs quantum (for electrons)-classical (for localized spins) dynamics in systems where nonequilibrium conduction electrons are present is lacking. Here we employ quantum Heisenberg F or AF chains of N = 4 sites, whose localized spins interact with conduction electrons via sd exchange interaction, to perform such comparison by starting from unentangled pure (at zero temperature) or mixed (at finite temperature) quantum state of localized spins as the initial condition. This reveals that quantum-classical dynamics can faithfully reproduce fully quantum dynamics in the F metallic case, but only when spin S, Heisenberg exchange between localized spins, and sd exchange are sufficiently small. Increasing any of these three parameters can lead to substantial deviations, which are explained by the dynamical buildup of entanglement between localized spins and/or between them and electrons. In the AF metallic case, substantial deviations appear even at early times, despite starting from an unentangled Neel state, which therefore poses a challenge on how to rigorously justify wide usage of the LL equation in phenomenological modeling of antiferromagnetic spintronics experiments. We also discuss finite temperature and finite size effects to demonstrate that: (i) including thermal fluctuations delays the onset of dynamical buildup of entanglement, but it does not suppress it; and (ii) no significant changes in the dynamics of this particular problem occur as we increase the chain length to N 4 sites, while even N = 4 is sufficient to observe quantum-chaotic energy level statistics whose emergence in such a small quantum many-body system crucially relies on the interaction between localized spins and conduction electrons.