Singh Hansveer, Ware Brayden A, Vasseur Romain, Friedman Aaron J
Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA.
Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA.
Phys Rev Lett. 2021 Dec 3;127(23):230602. doi: 10.1103/PhysRevLett.127.230602.
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_{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≃8/3.
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输运性质。利用随机酉电路，我们计算了系综平均光谱形状因子和线性响应相关函数，发现它们的特征时间尺度由有效哈密顿量的逆能隙给出，或者等效地，由描述经典马尔可夫过程的转移矩阵给出。我们的方法使我们能够直接将由光谱形状因子确定的 Thouless 时间(t_{Th})与输运性质和线性响应相关器联系起来。使用张量网络方法，我们确定了一些受约束的守恒模型的动力学指数(z)。我们发现了具有扩散、亚扩散、准局域化和局域化动力学的普适类，这取决于约束的严格程度。特别是，我们表明具有“弗雷德金”约束的量子系统表现出动力学指数(z\approx8/3)的反常输运。
