Operator growth in 2d CFT
arXiv:2110.10519 · doi:10.1007/JHEP12(2021)188
Abstract
We investigate and characterize the dynamics of operator growth in irrational two-dimensional conformal field theories. By employing the oscillator realization of the Virasoro algebra and CFT states, we systematically implement the Lanczos algorithm and evaluate the Krylov complexity of simple operators (primaries and the stress tensor) under a unitary evolution protocol. Evolution of primary operators proceeds as a flow into the 'bath of descendants' of the Verma module. These descendants are labeled by integer partitions and have a one-to-one map to Young diagrams. This relationship allows us to rigorously formulate operator growth as paths spreading along the Young's lattice. We extract quantitative features of these paths and also identify the one that saturates the conjectured upper bound on operator growth.
48 pages, 7 figures. v2: minor clarifications added, added fig. 4.1 and typos corrected
References in corpus (10)
- Operator complexity: a journey to the edge of Krylov space
- Krylov complexity in conformal field theory
- Random Matrix Theory for Complexity Growth and Black Hole Interiors
- Operator Delocalization in Quantum Networks
- A statistical mechanism for operator growth
- Semi-classical Virasoro blocks: proof of exponentiation
- Quantum operator growth bounds for kicked tops and semiclassical spin chains
- Six-point functions and collisions in the black hole interior
- Diagnosing collisions in the interior of a wormhole
- Complexity from Spinning Primaries
Cited by in corpus (17)
- Quantum chaos and the complexity of spread of states
- Krylov complexity in saddle-dominated scrambling
- Operator growth and Krylov construction in dissipative open quantum systems
- Operator growth in open quantum systems: lessons from the dissipative SYK
- Quantum complexity and topological phases of matter
- Krylov Complexity in Open Quantum Systems
- Krylov Complexity in Free and Interacting Scalar Field Theories with Bounded Power Spectrum
- Spread Complexity and Topological Transitions in the Kitaev Chain
- Krylov complexity in quantum field theory, and beyond
- Krylov complexity in large- and double-scaled SYK model
- Time evolution of spread complexity in quenched Lipkin-Meshkov-Glick model
- Entanglement and geometry from subalgebras of the Virasoro algebra
- Holographic Quantum Scars
- Chaos and operator growth in 2d CFT
- Virasoro Entanglement Berry Phases
- Collisions of localized shocks and quantum circuits
- Growth of a renormalized operator as a probe of chaos