Growth of a Renormalized Operator as a Probe of Chaos. (10th October 2022)

• Record Type: Journal Article
• Authors: Huang, Xing; Zhang, Binchao
• Other Names: Arzano Michele Academic Editor.
• Is Part Of: Advances in high energy physics. Volume 2022(2022)
• Publication Date: 2022-10-10
• Subjects: Particles (Nuclear physics) -- Periodicals; Particles (Nuclear physics); Periodicals; 539.76
• DOI: 10.1155/2022/9216427
• Languages: English
• ISSNs: 1687-7357

Abstract

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 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.