Scrambling and quantum chaos indicators from long-time properties of operator distributions
Scrambling and quantum chaos indicators from long-time properties of operator distributions
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DOI：
10.1103/physreva.107.032418
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发表时间：
2022-11
影响因子：
2.9
通讯作者：
S. Omanakuttan;K. Chinni;Philip Daniel Blocher;P. Poggi
中科院分区：
文献类型：
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作者：
S. Omanakuttan;K. Chinni;Philip Daniel Blocher;P. Poggi
在量子多体系统的非平衡性质分析中，无序是一个关键的概念。大多数研究都集中在它的表征通过out-of-time-ordered相关函数（OTOC），特别是通过早期的时间衰减的OTOC。然而，加扰是一个复杂的过程，其中涉及运营商传播和运营商纠缠，和一个完整的表征需要一个访问更精细的信息在几个时间尺度上的运营商动态。在这项工作中，我们分析了运营商扰码扩展的目标运营商在一个完整的基础上，并研究了作为一个粗粒度的概率分布在运营商空间的扩展系数的结构。我们研究了这种分布的不同特点，如其平均值，方差和参与率，伊辛模型与纵向和横向领域，踢集体自旋模型，和随机电路模型。我们表明，在这些情况下，运营商分布的长时间属性显示共同的功能，并讨论如何将这些属性可以作为一个代理的量子混沌的发病。最后，我们讨论了与OTOC的连接，并分析了使用这些相关函数实验探测运营商分布的成本。
Scrambling is a key concept in the analysis of nonequilibrium properties of quantum many-body systems. Most studies focus on its characterization via out-of-time-ordered correlation functions (OTOCs), particularly through the early-time decay of the OTOC. However, scrambling is a complex process which involves operator spreading and operator entanglement, and a full characterization requires one to access more refined information on the operator dynamics at several timescales. In this work we analyze operator scrambling by expanding the target operator in a complete basis and studying the structure of the expansion coefficients treated as a coarse-grained probability distribution in the space of operators. We study different features of this distribution, such as its mean, variance, and participation ratio, for the Ising model with longitudinal and transverse fields, kicked collective spin models, and random circuit models. We show that the long-time properties of the operator distribution display common features across these cases, and discuss how these properties can be used as a proxy for the onset of quantum chaos. Finally, we discuss the connection with OTOCs and analyze the cost of probing the operator distribution experimentally using these correlation functions.