Understanding universal aspects of quantum dynamics is an unresolved problem in statistical mechanics. In particular, the spin dynamics of the one-dimensional Heisenberg model were conjectured as to belong to the Kardar-Parisi-Zhang (KPZ) universality class based on the scaling of the infinite-temperature spin-spin correlation function. In a chain of 46 superconducting qubits, we studied the probability distribution of the magnetization transferred across the chain’s center, $P\left(\mathcal{M}\right)$. The first two moments of $P\left(\mathcal{M}\right)$ show superdiffusive behavior, a hallmark of KPZ universality. However, the third and fourth moments ruled out the KPZ conjecture and allow for evaluating other theories. Our results highlight the importance of studying higher moments in determining dynamic universality classes and provide insights into universal behavior in quantum systems.

中文翻译：

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海森堡自旋链中无限温度下的磁化动力学

理解量子动力学的普遍方面是统计力学中尚未解决的问题。特别是，基于无限温度自旋-自旋相关函数的缩放，一维海森堡模型的自旋动力学被推测属于 Kardar-Parisi-Zhang (KPZ) 普适类。在 46 个超导量子位的链中，我们研究了跨链中心转移的磁化强度的概率分布，$磷\left(\mathcal{中号}\right)$。前两个时刻$磷\left(\mathcal{中号}\right)$显示出超扩散行为，这是 KPZ 普遍性的标志。然而，第三和第四时刻排除了 KPZ 猜想并允许评估其他理论。我们的结果强调了研究更高矩在确定动态普遍性类别中的重要性，并为量子系统中的普遍行为提供了见解。