论文标题
部分可观测时空混沌系统的无模型预测
Ground-state and dynamical properties of a spin-$S$ Heisenberg star
论文作者
论文摘要
我们概括了海森堡恒星，该恒星由旋转1/2中央自旋和由XXX环建模的同质耦合的自旋浴[Richter J和Voigt A 1994 \ Emph {J。J。物理。答：数学。 gen.} \ textbf {27} 1139-1149]，与任意中央旋转大小$ s <n/2 $的情况，其中$ n $是浴缸的数量。我们描述了如何基于XXX环的Bethe Ansatz解决方案来阻止模型，并具有每个块Hamiltonian $ \ LEQ 2S+1 $的尺寸。我们在每个$ l $ -subspace中获得子地面状态的所有特征力和明确表达，$ l $是浴室的总角度动量。特征力和子地面国家都有不同的结构，具体取决于$ s \ leq l $还是$ l <s $。绝对地基状态和相应的$ l $作为内核耦合的功能是数值计算的，$ n = 16 $，$ s = 1,2，\ cdots，7 $，其行为在弱且强大的内部内核内耦合限制中进行了定量解释。然后，我们研究了在Néel状态制备的XXX浴中的抗铁磁顺序的动力学。研究了中央自旋的初始状态，$ s $的值以及系统浴耦合强度对交错磁化动力学的影响。通过在内部耦合中包括中央自旋和各向异性的zeeman项，我们还研究了中央自旋的极化动力学，用于在自旋相干状态下制备的浴缸。在浴室的共振条件下，在浴室的各向同性点上，$ s> 1/2 $的极化动力学表现出具有精细结构的倒塌复兴行为。然而，发现相对于内核内耦合的各向异性，塌陷复兴现象是脆弱的。
We generalize the Heisenberg star consisting of a spin-1/2 central spin and a homogeneously coupled spin bath modeled by the XXX ring [Richter J and Voigt A 1994 \emph{J. Phys. A: Math. Gen.} \textbf{27} 1139-1149] to the case of arbitrary central-spin size $S<N/2$, where $N$ is the number of bath spins. We describe how to block-diagonalize the model based on the Bethe ansatz solution of the XXX ring, with the dimension of each block Hamiltonian $\leq 2S+1$. We obtain all the eigenenergies and explicit expressions of the sub-ground states in each $l$-subspace with $l$ being the total angular momentum of the bath. Both the eigenenergies and the sub-ground states have distinct structures depending whether $S\leq l$ or $l<S$. The absolute ground-state energy and the corresponding $l$ as functions of the intrabath coupling are numerically calculated for $N=16$ and $S=1,2,\cdots,7$ and their behaviors are quantitatively explained in the weak and strong intrabath coupling limits. We then study the dynamics of the antiferromagnetic order within an XXX bath prepared in the Néel state. Effects of the initial state of the central spin, the value of $S$, and the system-bath coupling strength on the staggered magnetization dynamics are investigated. By including a Zeeman term for the central spin and the anisotropy in the intrabath coupling, we also study the polarization dynamics of the central spin for a bath prepared in the spin coherent state. Under the resonant condition and at the isotropic point of the bath, the polarization dynamics for $S>1/2$ exhibits collapse-revival behaviors with fine structures. However, the collapse-revival phenomena is found to be fragile with respect to anisotropy of the intrabath coupling.
