Chaos and operator growth in 2d CFT

Abstract

We study the out-of-time-ordered correlator (OTOC) in a zero temperature two dimensional conformal field theory (CFT) under evolution by a Liouvillian composed of the Virasoro generators. A bound was conjectured in arXiv:1812.08657 on the growth of the OTOC set by the Krylov complexity which is a measure of operator growth. The latter grows as an exponential of time with exponent $2\alpha$, which sets an upper bound on the Lyapunov exponent, ${\lambda }_L\le 2\alpha$. We find that for a two dimensional zero temperature CFT, the OTOC decays exponentially with a Lyapunov exponent which saturates this bound. We show that these Virasoro generators form the modular Hamiltonian of the CFT with half space traced out. Therefore, evolution by this modular Hamiltonian gives rise to thermal dynamics in a zero temperature CFT. Leveraging the thermal dynamics of the system, we derive this bound in a zero temperature CFT using the analyticity and boundedness properties of the OTOC.

arXiv comment21 pages, version published in JHEP

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Cited by in corpus (11)

• Universal chaotic dynamics from Krylov space
• Quantum Dynamics in Krylov Space: Methods and Applications
• Krylov complexity in quantum field theory, and beyond
• State Dependence of Krylov Complexity in $2d$ CFTs
• Entanglement and geometry from subalgebras of the Virasoro algebra
• Krylov complexity for non-local spin chains
• Universal Hypothesis of Autocorrelation Function from Krylov Complexity
• Entanglement wedge method, out-of-time-ordered correlators, and pole skipping
• Krylov Complexity in the Schrödinger Field Theory
• Information scrambling in quantum walks: Discrete-time formulation of Krylov complexity
• Krylov complexity and Wightman power spectrum with positive chemical potential in Schrödinger field theory