  We compute the scrambling rate at the antiferromagnetic (AFM) quantum
critical point, using the fixed point theory of Phys. Rev. X $\boldsymbol{7}$,
021010 (2017). At this strongly coupled fixed point, there is an emergent
control parameter $w \ll 1$ that is a ratio of natural parameters of the
theory. The strong coupling is unequally felt by the two degrees of freedom:
the bosonic AFM collective mode is heavily dressed by interactions with the
electrons, while the electron is only marginally renormalized. We find that the
scrambling rates act as a measure of the "degree of integrability" of each
sector of the theory: the Lyapunov exponent for the boson $\lambda_L^{(B)} \sim
\mathcal O(\sqrt{w}) \,k_B T/\hbar$ is significantly larger than the fermion
one $\lambda_L^{(F)} \sim \mathcal O(w^2) \,k_B T/\hbar$, where $T$ is the
temperature. Although the interaction strength in the theory is of order unity,
the larger Lyapunov exponent is still parametrically smaller than the universal
upper bound of $\lambda_L=2\pi k_B T/\hbar$. We also compute the spatial spread
of chaos by the boson operator, whose low-energy propagator is highly
non-local. We find that this non-locality leads to a scrambled region that
grows exponentially fast, giving an infinite "butterfly velocity" of the chaos
front, a result that has also been found in lattice models with long-range
interactions.
