Growth of a renormalized operator as a probe of chaos

• URL: http://arxiv.org/abs/2110.15306v2
• Date: Sat, 12 Nov 2022 05:51:54 GMT
• Title: Growth of a renormalized operator as a probe of chaos
• Authors: Xing Huang and Binchao Zhang
• Abstract summary: We propose that the size of an operator evolved under holographic renormalization group flow shall grow linearly with the scale. To test this conjecture, we study the operator growth in two different toy models.
• Score: 0.2741266294612776
• License: http://creativecommons.org/licenses/by/4.0/
• 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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