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arXiv · 2110.15306

Growth of a renormalized operator as a probe of chaos

Xing Huang·Binchao Zhang
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Abstract

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 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.

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Xing Huang, Binchao Zhang. 2021-10-28. Growth of a renormalized operator as a probe of chaos. https://doi.org/10.1155/2022%2F9216427

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