Information scrambling at an impurity quantum critical point

Abstract

The two-channel Kondo impurity model realizes a local non-Fermi liquid state with finite residual entropy. The competition between the two channels drives the system to an impurity quantum critical point. We show that the out-of-time-ordered (OTO) commutator for the impurity spin reveals markedly distinct behaviour depending on the low energy impurity state. For the one channel Kondo model with Fermi liquid ground state, the OTO commutator vanishes for late times, indicating the absence of the butterfly effect. For the two channel case, the impurity OTO commutator is completely temperature independent and saturates quickly to its upper bound 1/4, and the butterfly effect is maximally enhanced. These compare favourably to numerics on spin chain representation of the Kondo model. Our results imply that a large late time value of the OTO commutator does not necessarily diagnose quantum chaos.

8 pages, 6 figures

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• Out-of-time-ordered correlators of the Hubbard model: SYK strange metal in the spin freezing crossover region
• Information propagation in one-dimensional XY-$\Gamma$ chains
• Information Trapping by Topologically Protected Edge States: Scrambling and the Butterfly Velocity
• Fast quantum state preparation and bath dynamics using non-Gaussian variational ansatz and quantum optimal control
• Quantum Chaos of the Bose-Fermi Kondo model at the intermediate temperature
• Open quantum dynamics with variational non-Gaussian states and the truncated Wigner approximation
• Emergence of $X$ states in a quantum impurity model
• Scrambling Transition in Free Fermion Systems Induced by a Single Impurity