Many-body chaos in the antiferromagnetic quantum critical metal


Abstract in English

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 $lambda_L=2pi k_B T/hbar$. 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.

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