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The scrambling of quantum information in closed many-body systems, as measured by out-of-time-ordered correlation functions (OTOCs), has lately received considerable attention.
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This is in contrast with the biased diffusion process describing the dynamics of out-of-time-ordered correlators in random circuits without conserved quantities as described in previous work von Keyserlingk et al. 2017 ; Nahum et al. 2017 . In that case the diffusion constant was found to be a decreasing function of the local Hilbert space dimension q q . We emphasize that the diffusive broadening of OTOC front is different from the diffusion of conserved charge discussed in this section
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Note that this is different from the operator entanglement of the time evolution operator itself, wich is another proposed measure of chaotic behavior Zhou and Luitz 2017
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This is in contrast with the case without symmetries, where the sums in Eq. ( 14
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Note that the velocity v B ≈ 0.45 v_{B}\approx 0.45 observed here numerically is smaller than the butterfly velocity of a random circuit with the no symmetries and the same local Hilbert space dimension, derived to be 0.6 in Refs. von Keyserlingk et al. 2017 ; Nahum et al. 2017
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Tianci Zhou and David J. Luitz, “Operator entanglement entropy of the time evolution operator in chaotic systems,” Phys. Rev. B 95
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