Growth of a Renormalized Operator as a Probe of Chaos
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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
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| Series: | Advances in High Energy Physics |
| Online Access: | http://dx.doi.org/10.1155/2022/9216427 |
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| Summary: | 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. |
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| ISSN: | 1687-7365 |