We investigate the spectral and transport properties of many-body quantum systems with conserved charges and kinetic constraints. Using random unitary circuits, we compute ensemble-averaged spectral form factors and linear-response correlation functions, and find that their characteristic timescales are given by the inverse gap of an effective Hamiltonian—or equivalently, a transfer matrix describing a classical Markov process. Our approach allows us to connect directly the Thouless time, $t_{\text{Th}}$, determined by the spectral form factor, to transport properties and linear-response correlators. Using tensor network methods, we determine the dynamical exponent $z$ for a number of constrained, conserving models. We find universality classes with diffusive, subdiffusive, quasilocalized, and localized dynamics, depending on the severity of the constraints. In particular, we show that quantum systems with “Fredkin” constraints exhibit anomalous transport with dynamical exponent $z\simeq 8/3$.

中文翻译：

---

具有动力学约束的亚扩散和多体量子混沌

我们研究了具有守恒电荷和动力学约束的多体量子系统的光谱和传输特性。使用随机幺正电路，我们计算整体平均频谱形状因子和线性响应相关函数，并发现它们的特征时间尺度由有效哈密顿量的逆间隙给出——或者等效地，描述经典马尔可夫过程的传递矩阵。我们的方法使我们能够直接连接无神的时间，${吨}_{\text{钍}}$，由频谱形状因子决定，传输特性和线性响应相关器。使用张量网络方法，我们确定动态指数$z$对于许多受约束的、守恒的模型。我们根据约束的严重程度找到具有扩散、次扩散、准局部化和局部化动态的普适性类。特别是，我们表明具有“Fredkin”约束的量子系统表现出具有动态指数的异常输运$z\simeq 8/3$.