AI 中文总结
研究通过绘制迪克模型的复杂性相图，给出耦合强度\(g\)引发复杂性急剧转变的证据，识别并表征两种动力学 regime，阐明 regime 变化本质，其框架可应用于其他量子多体系统。
AI 中文摘要
调整相互作用量子系统的耦合强度\(g\)可能会使其基态或热性质发生突然变化。识别和掌握远离平衡动力学中的非解析甚至不连续转变更具挑战性。最近，克雷洛夫复杂性\(C_K\)为量子动力学中的算符增长、热化和混沌提供了新见解。但尚不清楚改变\(g\)是否以及如何能在复杂性度量中引发急剧转变。本文通过绘制描述与腔光子模式耦合的两能级原子的典型迪克模型的复杂性相图，给出了这种转变的证据。识别并表征了两种定性不同的动力学 regime。在转变处，\(C_K\)的斜率突然变化，与克雷洛夫熵的跃变一致。我们从克雷洛夫空间中的波包动力学阐明了 regime 变化的本质，其中一个粒子受大致线性势约束但跳跃时仿佛处于林德勒参考系。约束（导致反弹）与林德勒跳跃的解除约束（导致类似于引力拉伸的波包破坏）之间的竞争对兰索斯系数中的无序敏感。这里概述的框架可应用于其他量子多体系统。
英文摘要
Tuning the coupling strength $g$ of an interacting quantum system may drive a sudden change in its ground-state or thermal properties. To identify and grasp non-analytical, or even discontinuous, transitions in far-from-equilibrium dynamics proves more challenging. Recently Krylov complexity $C_K$ has offered fresh insights about operator growth, thermalization, and chaos in quantum dynamics. Yet it remains unclear if, and how, changing $g$ can trigger a sharp transition in the complexity measures. Here we present evidence for such a transition by mapping out the complexity phase diagram of the paradigmatic Dicke model describing two-level atoms coupled to a cavity photon mode. Two qualitatively different regimes of dynamics are identified and characterized. At the transition, the slope of $C_K$ changes suddenly to coincide with a jump in the Krylov entropy. We elucidate the nature of the regime change from the wave packet dynamics in Krylov space, where a particle is confined by a roughly linear potential but hops as if it lives in a Rindler reference frame. The competition between confinement, which leads to bouncing, and deconfinement by Rindler hopping, which leads to the destruction of wave packet analogous to gravitational spaghettification, is sensitive to the disorder in Lanczos coefficients. The framework outlined here can be applied to other quantum many-body systems.
Comments12 pages, 12 figures
