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.
Cited by 1
Xiao Chen et al., Quantum butterfly effect in polarized Floquet systems
Phys. Rev. B 101, 064307 (2020) [Crossref]