论文标题
高自旋XX中央自旋模型中的可分离和纠缠状态
Separable and entangled states in the high-spin XX central spin model
论文作者
论文摘要
在最近的预印本[Arxiv：2001.10008]中显示的是，具有XX型乘量子浴耦合的中央自旋模型可用于中央旋转$ S_0 = 1/2 $。体现了两种类型的本征态，可分离状态（黑暗状态）和中央自旋和浴缸之间的纠缠状态（明亮的状态）。在这项工作中，我们通过使用操作员产品状态方法显示，具有中央旋转$ S_0> 1/2 $和不均匀耦合的XX Central Spin模型可以部分解决。也就是说，特征状态的子集由操作员产品状态ANSATZ获得。这些是相对于完全极化的参考状态，在单旋转兴奋子空间中的可分离状态和纠缠状态。由于可分离状态的高变性，因此发现所得的bethe ansatz方程是非唯一的。在$ s_0 = 1/2 $的情况下，我们表明所有可分离状态和纠缠状态都可以根据操作员的产品状态编写，并在[Arxiv：2001.10008]中恢复结果。此外，我们还将我们的方法应用于均匀耦合的情况下，并得出相应的bethe ansatz方程。
It is shown in a recent preprint [arXiv:2001.10008] that the central spin model with XX-type qubit-bath coupling is integrable for a central spin $s_0=1/2$. Two types of eigenstates, separable states (dark states) and entangled states (bright states) between the central spin and the bath spins, are manifested. In this work, we show by using an operator product state approach that the XX central spin model with central spin $s_0>1/2$ and inhomogeneous coupling is partially solvable. That is, a subset of the eigenstates are obtained by the operator product state ansatz. These are the separable states and those entangled states in the single-spin-excitation subspace with respect to the fully polarized reference state. Due to the high degeneracy of the separable states, the resulting Bethe ansatz equations are found to be non-unique. In the case of $s_0=1/2$ we show that all the separable and entangled states can be written in terms of the operator product states, recovering the results in [arXiv:2001.10008]. Moreover, we also apply our method to the case of homogeneous coupling and derive the corresponding Bethe ansatz equations.
