Krylov空间中受监测SSH模型的动力学：从复杂度到量子Fisher信息
Dynamics of monitored SSH Model in Krylov Space: From Complexity to Quantum Fisher Information
AI总结：
本文研究受监测SSH模型在Krylov空间中的非厄米动力学，发现复杂度饱和时间随测量率增加，其子系统标度在PT转变点出现不连续跳跃，并证明量子Fisher信息可作为测量诱导相的有效探针。
摘要：
在本文中，我们研究了非厄米SSH模型的动力学，该模型源于受监测SSH模型在Krylov空间中的无点击极限。我们发现，与态在Krylov子空间中扩散相关的复杂度的饱和时间尺度随测量率的增加而增加，并且其晚期行为在PT对称转变点两侧表现出差异。此外，将这种复杂度的概念推广到Krylov空间中的子系统，我们发现其晚期值随子系统尺寸的标度在PT转变点处显示出不连续的跳跃，表明它可以用作该转变的合适序参量，但不能用于测量诱导的转变。最后，我们证明了Krylov子空间中的一种广义度量，它包含关联景观的信息，例如量子Fisher信息，其本身也与复杂度泛函具有某些结构相似性，可以成为测量诱导相的一个有前景的探针。
英文摘要：
In this paper, we investigate the dynamics of a non-Hermitian SSH model that arises out of the no-click limit of a monitored SSH model in the Krylov space. We find that the saturation timescale of the complexity associated with the spread of the state in the Krylov subspace increases with the measurement rate, and late time behaviour differs across the $\mathrm{PT}$ symmetry transition point. Furthermore, extending the notion of this complexity for subsystems in Krylov space, we find that the scaling of its late time value with subsystem size shows a discontinuous jump across the $\mathrm{PT}$ transition point, indicating that it can be used as a suitable order parameter for such transition but not for the measurement-induced transition. Finally, we show that a generalized measure in the Krylov subspace, which contains information about the correlation landscape, such as Quantum Fisher information, which also possesses some structural similarity with the complexity functional, can be a promising probe of the measurement-induced phase.
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