横向场中 XX 自旋-1 中心自旋模型的可积性与暗态
Integrability and dark states of the XX spin-1 central spin model in a transverse field
AI总结：
本文证明自旋-1 XX 中心自旋模型在倾斜磁场下仍可积，给出完整守恒荷及其多项式关系，并数值验证强耦合下存在中心自旋与浴无纠缠的暗态。
摘要：
近期研究表明，对于中心自旋-1/2 和中心自旋-1，当存在垂直于耦合所在 XY 平面的磁场时，XX 中心自旋模型是可积的。在自旋-1/2 情形中，通过对非斜对称 XXZ Richardson-Gaudin 模型取适当极限，还表明即使磁场倾斜而包含面内分量，该模型仍保持可积。尽管该模型尚未被明确证明属于已知的 Richardson-Gaudin 模型类别，但我们在本工作中证明，自旋-1 情形在倾斜磁场中也仍保持可积。为此，我们显式写出完整的守恒荷集合，随后证明这些算符满足多项式关系。最后通过数值计算证明，当耦合足够强时，可能出现中心自旋与浴完全无纠缠的暗态，正如任意取向磁场中的中心自旋-1/2 模型所表现的那样。
英文摘要：
It was recently shown that, for central spin-1/2 and central spin-1, the XX central spin model is integrable in the presence of a magnetic field oriented perpendicular to the XY plane in which the coupling exists. In the spin-1/2 case, it was also shown, through an appropriate limit of the non-skew symmetric XXZ Richardson-Gaudin models, that it remained integrable even when the magnetic field is tilted to contain an in-plane component. Although the model has not yet been shown to explicitly belong to a known class of Richardson- Gaudin models, we show, in this work, that the spin-1 case also remains integrable in a titled magnetic field. We do so by writing explicitly the complete set of conserved charges, then showing that these operators obey polynomial relations. It is finally demonstrated numerically that dark states, for which the central spin is completely unentangled with the bath, can emerge at strong enough coupling just as they do in the central spin-1/2 model in an arbitrarily oriented magnetic field.
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