Growth of a renormalized operator as a probe of chaos
arXiv:2110.15306 · doi:10.1155/2022/9216427
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.
arXiv comment20 pages, 3 figures; v2: typos fixed, published version
References in corpus (27)
- A bound on chaos
- The ITensor Software Library for Tensor Network Calculations
- Entanglement Renormalization and Holography
- Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
- Bulk Locality and Quantum Error Correction in AdS/CFT
- Quantum Entanglement Growth Under Random Unitary Dynamics
- Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality
- Relative entropy equals bulk relative entropy
- A Universal Operator Growth Hypothesis
- Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT
- Chaos, Complexity, and Random Matrices
- Anti-de Sitter Space from Optimization of Path Integrals in Conformal Field Theories
- Operator growth in the SYK model
- Surface/State Correspondence as a Generalized Holography
- A quantum hydrodynamical description for scrambling and many-body chaos
- Quantum Epidemiology: Operator Growth, Thermal Effects, and SYK
- Random Matrix Theory for Complexity Growth and Black Hole Interiors
- Complexity for Conformal Field Theories in General Dimensions
- Operator growth in 2d CFT
- From Path Integrals to Tensor Networks for AdS/CFT
- Quantum Criticality and the Kondo Lattice
- Constructing holographic spacetimes using entanglement renormalization
- CFT descriptions of bulk local states in the AdS black holes
- On systems of maximal quantum chaos
- Complexity and Momentum
- Scrambling and Lyapunov Exponent in Unitary Networks with Tunable Interactions
- Entanglement renormalization and integral geometry