论文标题
量子运算符的生长界和半经典旋转链的生长界
Quantum operator growth bounds for kicked tops and semiclassical spin chains
论文作者
论文摘要
我们提出了一个框架，以理解运算符大小的动态，并在大型$ s $ spins的模型中限制了超时订购的相关器的增长。为了关注单个旋转的动力，我们在巨大的$ s $限制中显示了Lyapunov指数的有限性；我们的边界比这些系统上最知名的Lieb-Robinson型界限更紧密。我们从数值上发现我们在Lyapunov指数上的上限在经典和量子踢的顶部模型中数值计算值的数量级。将我们的结果推广到晶格上的大$ S $旋转，我们表明，蝴蝶速度的特征是量子信息的空间速度争夺，这是$ s \ rightarrow \ rightarrow \ infty $。我们强调了在半经典大型旋转模型中运营商增长与包括Sachdev-Ye-Kitaev模型在内的量子全息系统之间的定性差异。
We present a framework for understanding the dynamics of operator size, and bounding the growth of out-of-time-ordered correlators, in models of large-$S$ spins. Focusing on the dynamics of a single spin, we show the finiteness of the Lyapunov exponent in the large-$S$ limit; our bounds are tighter than the best known Lieb-Robinson-type bounds on these systems. We numerically find our upper bound on Lyapunov exponents is within an order of magnitude of numerically computed values in classical and quantum kicked top models. Generalizing our results to coupled large-$S$ spins on lattices, we show that the butterfly velocity, which characterizes the spatial speed of quantum information scrambling, is finite as $S\rightarrow\infty$. We emphasize qualitative differences between operator growth in semiclassical large-spin models, and quantum holographic systems including the Sachdev-Ye-Kitaev model.
