Data for ''Fading ergodicity and quantum dynamics in random matrix ensembles''

Recent work has proposed fading ergodicity as a mechanism for many-body ergodicity breaking. Here, we show that two paradigmatic random matrix ensembles -- the Rosenzweig–Porter model and the ultrametric model -- fall within the same universality class of ergodicity breaking when embedded in a many-body Hilbert space of spins-1/2. By calibrating the parameters of both models via their Thouless times, we demonstrate that the matrix elements of local observables display similar statistical properties, allowing us to identify the fractal phase of the Rosenzweig–Porter model with the fading-ergodicity regime. This correspondence is further supported through the analyses of quantum-quench dynamics of local observables, their temporal fluctuations and power spectra, and survival probabilities. Our findings reveal that local observables thermalize within the fading-ergodicity regime on timescales shorter than the Heisenberg time, thus providing a unified framework for understanding ergodicity breaking across these distinct models.近期研究提出，渐逝遍历性（fading ergodicity）可作为多体遍历性破缺的一种机制。本文证明，两类典型的随机矩阵系综——罗森茨魏希-波特（Rosenzweig–Porter）模型与超度量（ultrametric）模型——在嵌入自旋1/2的多体希尔伯特空间后，同属于遍历性破缺的同一普适类。我们通过杜洛斯时间（Thouless time）对两个模型的参数进行校准，结果表明局域可观测量的矩阵元展现出相似的统计特性，由此可将罗森茨魏希-波特模型的分形相与渐逝遍历性区域相对应。这一对应关系还得到了多维度分析的进一步支撑：对局域可观测量的量子淬火动力学、其时间涨落与功率谱以及存活概率的分析。我们的研究发现显示，在短于海森堡时间的时间尺度内，局域可观测量会在渐逝遍历性区域内实现热化，从而为理解这类不同模型中的遍历性破缺提供了统一的理论框架。