Bound on the exponential growth rate of out-of-time-ordered correlators

Abstract

It has been conjectured by Maldacena, Shenker, and Stanford [J. High Energy Phys.~08 (2016) 106] that the exponential growth rate of the out-of-time-ordered correlator (OTOC) $F(t)$ has a universal upper bound $2\pi k_{B}T/\hslash$. Here we introduce a one-parameter family of out-of-time-ordered correlators $F_{\gamma }(t)$ ($0\le \gamma \le 1$), which has as good properties as $F(t)$ as a regularization of the out-of-time-ordered part of the squared commutator $⟨[A(t),B(0){]}^2⟩$ that diagnoses quantum many-body chaos, and coincides with $F(t)$ at $\gamma =1/2$. We rigorously prove that if $F_{\gamma }(t)$ shows a transient exponential growth for all $\gamma$ in $0\le \gamma \le 1$, that is, if the OTOC shows an exponential growth regardless of the choice of the regularization, then the growth rate $\lambda$ does not depend on the regularization parameter $\gamma$, and satisfies the inequality $\lambda \le 2\pi k_{B}T/\hslash$.

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• Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
• Nonlinear sigma model approach to many-body quantum chaos: Regularized and unregularized out-of-time-ordered correlators
• Bounds in Nonequilibrium Quantum Dynamics
• Thermal Emission from Semi-classical Dynamical Systems
• Verifying the upper bound on the speed of scrambling with the analogue Hawking radiation of trapped ions
• Quantum bounds and fluctuation-dissipation relations
• Spectral Form Factor as an OTOC Averaged over the Heisenberg Group
• Decay of a Thermofield-Double State in Chaotic Quantum Systems
• Quantum chaos without false positives
• Refined quantum Lyapunov exponents from replica out-of-time-order correlators
• Quantum bounds on the generalized Lyapunov exponents
• Bound on Lyapunov exponent in Einstein-Maxwell-Dilaton-Axion black holes
• BROTOCs and Quantum Information Scrambling at Finite Temperature
• Microcanonical windows on quantum operators
• Out-of-time-ordered correlators of the Hubbard model: SYK strange metal in the spin freezing crossover region
• Analyticity constraints bound the decay of the spectral form factor
• Sensitivity to the initial conditions of the Time-Dependent Density Functional Theory
• Early-Time and Late-Time Quantum Chaos
• Thermalization of horizon through asymptotic symmetry in three-dimensional massive gravity
• Quantum Chaos in Non-Markovian Open Quantum Systems: Interferometric OTOC, Loschmidt Echo and Commutator Operator Norm
• Bound on Lyapunov exponent in $c=1$ matrix model
• Out-of-time-ordered commutators in Dirac--Weyl systems
• Interferometric and Bipartite OTOC for Non-Markovian Open Quantum Spin-Chains and Lipkin-Meshkov-Glick Model