We propose that the size of an operator evolved under holographic renormalization group flow shall grow linearly with the scale and interpret this behavior as a manifestation of the saturation of the chaos bound. To test this conjecture, we study the operator growth in two different toy models. The first one is a MERA-like tensor network built from a random unitary circuit with the operator size defined using the integrated out-of-time-ordered correlator (OTOC). The second model is an error-correcting code of perfect tensors, and the operator size is computed using the number of single-site physical operators that realize the logical operator. In both cases, we observe linear growth.

中文翻译：

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作为混沌探测的重整化算子的增长

我们建议在全息重整化群流下演化的算子的大小应随尺度线性增长，并将这种行为解释为混沌界限饱和的表现。为了验证这个猜想，我们研究了两种不同玩具模型中的算子增长。第一个是一个类似 MERA 的张量网络，它由一个随机单一电路构建，其算子大小使用集成的时间无序相关器 (OTOC) 定义。第二种模型是完美张量的纠错码，使用实现逻辑算子的单点物理算子的数量来计算算子大小。在这两种情况下，我们都观察到线性增长。