# Information scrambling at an impurity quantum critical point

## TL;DR

This paper investigates how the out-of-time-ordered commutator behaves at an impurity quantum critical point, revealing distinct signatures of quantum chaos and non-Fermi liquid states in the two-channel Kondo model.

## Contribution

It demonstrates that the impurity OTO commutator exhibits maximal saturation at the quantum critical point, contrasting with Fermi liquid behavior, and challenges the use of late-time OTO values as chaos indicators.

## Key findings

- OTOC commutator saturates to 1/4 in the two-channel case
- Late-time OTO value does not necessarily indicate chaos
- Numerical results support theoretical predictions

## 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.