On the evolution of operator complexity beyond scrambling
By J. Barbón, E. Rabinovici, R. Shir, R. Sinha. Journal of High Energy Physics, 2019
188 citations recorded by the source corpus.
A bstractWe study operator complexity on various time scales with emphasis on those much larger than the scrambling period. We use, for systems with a large but finite number of degrees of freedom, the notion of K-complexity employed in [1] for infinite systems. We present evidence that K-complexity of ETH operators has indeed the character associated with the bulk time evolution of extremal volumes and actions. Namely, after a period of exponential growth during the scrambling period the K-complexity increases only linearly with time for exponentially long times in terms of the entropy, and it eventually saturates at a constant value also exponential in terms of the entropy. This constant value depends on the Hamiltonian and the operator but not on any extrinsic tolerance parameter. Thus K-complexity deserves to be an entry in the AdS/CFT dictionary. Invoking a concept of K-entropy and some numerical examples we also discuss the extent to which the long period of linear complexity growth entails an efficient randomization of operators.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a32fa3a44cf140c5bb0d417f363770fcc21288b2
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
In Mathematical Physics
Citations in the corpus
- Krylov complexity in conformal field theory (2021, background): “At the level of definition it is not re-lated to circuit complexity, but a number of recent works [10–12] found qualitative agreement between the behavior of K O ( t ) with the behavior of circuit and holographic complexities [13].”
- Krylov complexity in saddle-dominated scrambling (2022, unknown): “At very late times, b n decreases to zero when the whole Krylov space is exhausted, and as a result, the K-complexity saturates [38, 42].”
- Krylov complexity from integrability to chaos (2022, background): “We will focus on K-complexity at long time scales for finite systems away from the thermodynamic limit [4, 5, 7].”