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Quantum scrambling and state dependence of the butterfly velocity

Xizhi Han (韩希之), Sean A. Hartnoll

SciPost Phys. 7, 045 (2019) · published 8 October 2019


Operator growth in spatially local quantum many-body systems defines a scrambling velocity. We prove that this scrambling velocity bounds the state dependence of the out-of-time-ordered correlator in local lattice models. We verify this bound in simulations of the thermal mixed-field Ising spin chain. For scrambling operators, the butterfly velocity shows a crossover from a microscopic high temperature value to a distinct value at temperatures below the energy gap.

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Quantum many-body systems

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