淬火 LMG 模型中的 Krylov 复杂度与动力学相变
Krylov Complexity and Dynamical Phase Transition in the quenched LMG model
AI总结：
本文数值研究 LMG 模型淬火后的 Krylov 复杂度，证明其长期平均值可作为区分两种动力学相的序参量，并借助基矢等价性解释不同复杂度指标的一致性。
摘要：
研究量子系统中复杂度的时间演化，需要评估系统状态在其相应 Hilbert 空间中沿给定基矢的扩展。最近，Krylov 基被确定为使这种扩展最小化的基。在本研究中，我们对 Lipkin-Meshkov-Glick 模型在淬火后量子态的 Krylov 复杂度进行了数值探索。结果表明，长期平均 Krylov 复杂度可作为该模型的序参量。它能有效区分淬火诱导的两种动力学相，并与常规序参量共享同一个临界点。此外，我们还考察了 Krylov 基和能量基中的逆参与比和 Shannon 熵。当初始态具有某种特定对称性时，两种基中可观察到一致的动力学行为。通过建立 Krylov 基与淬火前能量本征基之间的等价性，我们对这一行为给出了解析解释。
英文摘要：
Investigating the time evolution of complexity in quantum systems entails evaluating the spreading of the system's state across a defined basis in its corresponding Hilbert space. Recently, the Krylov basis has been identified as the one that minimizes this spreading. In this study, we develop a numerical exploration of the Krylov complexity in quantum states following a quench in the Lipkin-Meshkov-Glick model. Our results reveal that the long-term averaged Krylov complexity acts as an order parameter for this model. It effectively discriminates between the two dynamic phases induced by the quench, sharing a critical point with the conventional order parameter. Additionally, we examine the inverse participation ratio and the Shannon entropy in both the Krylov basis and the energy basis. A matching dynamic behavior is observed in both bases when the initial state possesses a specific symmetry. This behavior is analytically explained by establishing the equivalence between the Krylov basis and the pre-quench energy eigenbasis.
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