自旋-1中心自旋XX模型的可积性与淬火动力学
Integrability and quench dynamics in the spin-1 central spin XX model
AI总结：
本文证明了自旋-1中心自旋XX模型具有可积性，利用Bethe ansatz推导出守恒量与精确本征态，揭示了亮态与暗态在淬火动力学中阻止热平衡的机制，并猜想任意自旋$s$的该模型均可积。
摘要：
中心自旋模型为中心自由度与周围自旋的介观环境之间的相互作用提供了一种理想化的描述。我们证明，中心为自旋-1且与周围自旋具有任意强度XX相互作用的模型族是可积的。具体而言，我们推导出了一套广泛的守恒量，并利用Bethe ansatz获得了精确的本征态。如同在均匀极限下一样，这些态分为两个指数级大的类别：亮态（其中自旋-1与其周围环境纠缠）和暗态（其中自旋-1不与周围环境纠缠）。在共振条件下，亮态根据其在中心自旋极化为零的态上的权重进一步分为两类。这些类别在淬火动力学中得到了探究，在其中它们阻止中心自旋达到热平衡。在单自旋翻转区，我们显式构造了亮态，并表明由于这些本征态的半局域化，中心自旋表现出振荡动力学。我们将该可积性与密切相关的可积Richardson-Gaudin模型类联系起来，并猜想对于任意$s$，自旋-$s$中心自旋XX模型都是可积的。
英文摘要：
Central spin models provide an idealized description of interactions between a central degree of freedom and a mesoscopic environment of surrounding spins. We show that the family of models with a spin-1 at the center and XX interactions of arbitrary strength with surrounding spins is integrable. Specifically, we derive an extensive set of conserved quantities and obtain the exact eigenstates using the Bethe ansatz. As in the homogenous limit, the states divide into two exponentially large classes: bright states, in which the spin-1 is entangled with its surroundings, and dark states, in which it is not. On resonance, the bright states further break up into two classes depending on their weight on states with central spin polarization zero. These classes are probed in quench dynamics wherein they prevent the central spin from reaching thermal equilibrium. In the single spin-flip sector we explicitly construct the bright states and show that the central spin exhibits oscillatory dynamics as a consequence of the semilocalization of these eigenstates. We relate the integrability to the closely related class of integrable Richardson-Gaudin models, and conjecture that the spin-$s$ central spin XX model is integrable for any $s$.
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