Krylov complexity in conformal field theory
By Anatoly Dymarsky, M. Smolkin. Physical Review D, 2021
167 citations recorded by the source corpus.
Krylov complexity, or K-complexity for short, has recently emerged as a new probe of chaos in quantum systems. It is a measure of operator growth in Krylov space, which conjecturally bounds the operator growth measured by the out of time ordered correlator (OTOC). We study Krylov complexity in conformal field theories by considering arbitrary 2d CFTs, free field, and holographic models. We find that the bound on OTOC provided by Krylov complexity reduces to bound on chaos of Maldacena, Shenker, and Stanford. In all considered examples including free and rational CFTs Krylov complexity grows exponentially, in stark violation of the expectation that exponential growth signifies chaos.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/8cd1206b34cc41c88dd31349e2e11c9b0eabcc4c
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In Atomic and Molecular Physics, and Optics
- J. Sonner
- R. Shir
- E. Rabinovici
- A. Sánchez-Garrido
- Javier M. Magán
- Dimitrios Patramanis
- Paweł Caputa
In Condensed Matter Physics
- Javier M. Magán
- R. Shir
- A. Sánchez-Garrido
- E. Rabinovici
- Dimitrios Patramanis
- Paweł Caputa
- J. Sonner
In Nuclear and High Energy Physics
- J. Sonner
- Javier M. Magán
- R. Shir
- A. Sánchez-Garrido
- E. Rabinovici
- Dimitrios Patramanis
- Paweł Caputa
Citations in the corpus
- Geometry of Krylov complexity (2021, background): “Note that this generalization to 2d CFTs seems completely determined by symmetries (see more discussion in [30]).”
- Krylov complexity from integrability to chaos (2022, methodology): “In addition to the behavior of K-complexity for given individual quantum systems, such as the SYK model [3, 5, 6], 2D CFTs [18, 19], and more general symmetry-based Hamiltonian systems [20, 21], it is interesting and important to categorize the possible Krylov phenomenologies according to more unive”