Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA, 93106, USA.
Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA.
Nat Commun. 2023 Jun 9;14(1):3411. doi: 10.1038/s41467-023-39065-5.
In chaotic many-body systems, scrambling or the operator growth can be diagnosed by out-of-time-order correlators of local operators. We show that operator growth also has a sharp imprint in out-of-time-order correlators of global operators. In particular, the characteristic spacetime shape of growing local operators can be accessed using global measurements without any local control or readout. Building on an earlier conjectured phase diagram for operator growth in chaotic systems with power-law interactions, we show that existing nuclear spin data for out-of-time-order correlators of global operators are well fit by our theory. We also predict super-polynomial operator growth in dipolar systems in 3d and discuss the potential observation of this physics in future experiments with nuclear spins and ultra-cold polar molecules.
在混沌多体系统中，可以通过局域算符的时间非关联相关函数来诊断混叠或算子增长。我们表明，算子增长在全局算符的时间非关联相关函数中也有明显的印记。具体来说，利用全局测量而无需任何局部控制或读出，可以获得增长的局域算子的特征时空形状。基于先前对于具有幂律相互作用的混沌系统中的算子增长的相位图的一个猜想，我们表明，现有的关于全局算子的时间非关联相关函数的核自旋数据很好地符合我们的理论。我们还预测了三维偶极系统中的超多项式算子增长，并讨论了在未来的核自旋和超冷极性分子实验中观测这一物理现象的可能性。
