A two-way approach to out-of-time-order correlators

Abstract

Out-of-time-order correlators (OTOCs) are a standard measure of quantum chaos. Of the four operators involved, one pair may be regarded as a source and the other as a probe. A usual approach, applicable to large-$N$ systems such as the SYK model, is to replace the actual source with some mean-field perturbation and solve for the probe correlation function on the double Keldysh contour. We show how to obtain the OTOC by combining two such solutions for perturbations propagating forward and backward in time. These dynamical perturbations, or scrambling modes, are considered on the thermofield double background and decomposed into a coherent and an incoherent part. For the large-$q$ SYK, we obtain the OTOC in a closed form. We also prove a previously conjectured relation between the Lyapunov exponent and high-frequency behavior of the spectral function.

arXiv comment37 pages, 9 figures. v2: a typo fixed, a reference added. v3: two typos fixed, a reference added. v4: presentation improved, more references added

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Cited by in corpus (11)

• Eigenstate Thermalization Hypothesis and Free Probability
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• Krylov complexity in quantum field theory, and beyond
• Krylov complexity in large-$q$ and double-scaled SYK model
• Dynamical Transition of Operator Size Growth in Quantum Systems Embedded in an Environment
• Out-of-Time-Order correlators in driven conformal field theories
• Chaos and operator growth in 2d CFT
• Disordered vector models: from higher spins to incipient strings
• Operator Size Distribution in Large $N$ Quantum Mechanics of Majorana Fermions
• Quantum Error Correction in SYK and Bulk Emergence
• Notes on Wormhole Cancellation and Factorization