In this paper, we explore the decoherence dynamics of a probing spin coupled to a spin bath, where the spin bath is given by a controllable 1D transverse-field Ising chain. The 1D transverse-field Ising chain with free-ends boundary condition is equivalent to a modified Kitaev model with non-local Majorana bound states in its topological phase. We find that the non-Markovian decoherence dynamics of the probing spin can manifest the topological structure of the spin chain. By controlling the external magnetic field on the Ising chain, we find a close relationship between the topological phase transition and the non-Markovian dynamics in the real-time domain. We also investigate the corresponding quantum entanglement dynamics in this topological system.

中文翻译：

---

通过实时域中与自旋浴耦合的自旋的精确非马尔可夫退相干动力学来探测拓扑状态

在本文中，我们探索了与自旋浴耦合的探测自旋的退相干动力学，其中自旋浴由可控的一维横向场伊辛链给出。具有自由端边界条件的一维横向场Ising链等效于在其拓扑阶段具有非局部Majorana束缚态的改良Kitaev模型。我们发现探测自旋的非马尔可夫退相干动力学可以体现自旋链的拓扑结构。通过控制伊辛链上的外部磁场，我们发现了拓扑相变与实时域中的非马尔可夫动力学之间的密切关系。我们还研究了该拓扑系统中相应的量子纠缠动力学。