论文标题
与可调互动的统一网络中的争夺和Lyapunov指数
Scrambling and Lyapunov Exponent in Unitary Networks with Tunable Interactions
论文作者
论文摘要
通过超时订购的相关器（OTOC）量化的量子多体系统中的信息是量子混乱的关键表现。到目前为止，在具有高维当地希尔伯特空间和弱耦合系统的系统中，以Lyapunov指数为特征的OTOC的指数增长制度大多是在大多数情况下观察到的。在这里，我们提出了一个通用标准，即存在与局部相互作用的空间扩展系统中OTOC指数增长的明确定义的状态。在这样的系统中，我们表明，长期的指数增长期要求蝴蝶速度比Lyapunov指数大得多，诸如晶格间距等显微镜长度尺度。作为一个明确的例子，我们研究了具有可调相互作用的随机统一电路。在此模型中，我们表明，在弱相互作用的限制中，满足了上述标准，并且有一个长时间的指数增长窗口。我们的结果基于分析处理支持的Clifford和通用随机电路的数值模拟。
Scrambling of information in a quantum many-body system, quantified by the out-of-time-ordered correlator (OTOC), is a key manifestation of quantum chaos. A regime of exponential growth in the OTOC, characterized by a Lyapunov exponent, has so far mostly been observed in systems with a high-dimensional local Hilbert space and in weakly-coupled systems. Here, we propose a general criterion for the existence of a well-defined regime of exponential growth of the OTOC in spatially extended systems with local interactions. In such systems, we show that a parametrically long period of exponential growth requires the butterfly velocity to be much larger than the Lyapunov exponent times a microscopic length scale, such as the lattice spacing. As an explicit example, we study a random unitary circuit with tunable interactions. In this model, we show that in the weakly interacting limit the above criterion is satisfied, and there is a prolonged window of exponential growth. Our results are based on numerical simulations of both Clifford and universal random circuits supported by an analytical treatment.
