Anomalous subdiffusion from subsystem symmetries
Anomalous subdiffusion from subsystem symmetries
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DOI：
10.1103/physrevb.100.214301
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发表时间：
2019-12-04
影响因子：
3.7
通讯作者：
Nandkishore, Rahul
中科院分区：
文献类型：
--
作者：
Iaconis, Jason;Vijay, Sagar;Nandkishore, Rahul
我们介绍量子电路在两个和三个空间维度是经典的模拟，尽管产生了高度的运营商纠缠。我们提供了这些“自动机”量子电路的部分表征，并使用它们来研究子系统对称性的量子动力学中的算子增长，信息传播和局部电荷弛豫，我们定义为作用于低维子流形的重叠对称性。有了这些对称性，我们发现了保守电荷的反常次扩散，也就是说，电荷在子系统对称性的维度上扩散得比扩散慢。通过研究存在这些对称性的有效算子流体力学，我们预测电荷自相关器在二维中衰减为ln（t）/root t，其中U（1）电荷沿着相交线守恒;在三维空间中衰减为1/t（3/4），其中平面U（1）对称性相交。通过对具有这些对称性的自动机动力学的大规模研究，我们在数值上观察到与这些预测一致的电荷弛豫。在这两种情况下，空间电荷分布是明显的非高斯的，并让人联想到电荷沿着分形表面的扩散。我们数值研究这些自动机动力学下的局部算子的传播量子混沌的发病，并观察幂律扩大的弹道传播前沿的不断发展的运营商在二维和三维和饱和度的时间有序的相关性的值符合量子混沌行为。
We introduce quantum circuits in two and three spatial dimensions which are classically simulable, despite producing a high degree of operator entanglement. We provide a partial characterization of these "automaton" quantum circuits and use them to study operator growth, information spreading, and local charge relaxation in quantum dynamics with subsystem symmetries, which we define as overlapping symmetries that act on lower-dimensional submanifolds. With these symmetries, we discover the anomalous subdiffusion of conserved charges; that is, the charges spread slower than diffusion in the dimension of the subsystem symmetry. By studying an effective operator hydrodynamics in the presence of these symmetries, we predict the charge autocorrelator to decay (i) as ln(t)/root t in two dimensions with a conserved U(1) charge along intersecting lines and (ii) as 1/t(3/4 )in three spatial dimensions with intersecting planar U(1) symmetries. Through large-scale studies of automaton dynamics with these symmetries, we numerically observe charge relaxation that is consistent with these predictions. In both cases, the spatial charge distribution is distinctly non-Gaussian and reminiscent of the diffusion of charges along a fractal surface. We numerically study the onset of quantum chaos in the spreading of local operators under these automaton dynamics and observe power-law broadening of the ballistically propagating fronts of evolving operators in two and three dimensions and the saturation of out-of-time-ordered correlations to values consistent with quantum chaotic behavior.