Quantum Scrambling and State Dependence of the Butterfly Velocity
arXiv:1812.07598 · doi:10.21468/SciPostPhys.7.4.045
Abstract
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.
arXiv comment13 pages + appendices, 3 + 6 figures. v3: improved presentation
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