标题： 抗集中和遍历量子动力学下的魔法传播 显示英文标题

标题： Anticoncentration and magic spreading under ergodic quantum dynamics

摘要： 量子态复杂性度量，如抗集中和魔法，为多体物理、信息扰乱和量子计算提供了关键见解。抗集中和魔法在随机量子电路动力学下的均衡化以与系统大小对数相关的时间尺度发生，这一预测被认为适用于更广泛的遍历动力学。 本研究通过检查一维遍历Floquet模型和哈密顿系统的抗集中和魔法传播，挑战了这一观点。使用参与熵和稳定子熵来探测这些资源，我们揭示了在这两种设置之间存在显著差异。Floquet系统与随机电路的预测一致，在时间尺度上以对数方式随系统大小增加表现出抗集中和魔法饱和。相比之下，哈密顿动力学偏离了随机电路的预测，并且需要大约线性于系统大小的时间尺度才能实现参与熵和稳定子熵的饱和，即使在长时间极限下，这些熵仍然小于典型量子态的熵。我们的发现确立了遍历多体系统中参与和熵增长的现象学，并强调了能量守恒在限制抗集中和魔法动态中的作用。 显示英文摘要

摘要： Quantum state complexity metrics, such as anticoncentration and magic, offer key insights into many-body physics, information scrambling, and quantum computing. Anticoncentration and equilibration of magic under dynamics of random quantum circuits occur at times scaling logarithmically with system size, a prediction that is believed to extend to more general ergodic dynamics. This work challenges this idea by examining the anticoncentration and magic spreading in one-dimensional ergodic Floquet models and Hamiltonian systems. Using participation and stabilizer entropies to probe these resources, we reveal significant differences between the two settings.Floquet systems align with random circuit predictions, exhibiting anticoncentration and saturation of magic at time scales that increase logarithmically with system size. In contrast, Hamiltonian dynamics deviate from the random circuit predictions and require times scaling approximately linearly with system size to achieve saturation of participation and stabilizer entropies, which remain smaller than that of the typical quantum states even in the long-time limit. Our findings establish the phenomenology of participation and entropy growth in ergodic many-body systems and emphasize the role of energy conservation in constraining anticoncentration and magic dynamics.