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  • Open Access

Fast Scrambling at the Boundary

Ancel Larzul1, Anirvan M. Sengupta2,3,4, Antoine Georges3,5,6,7, and Marco Schirò1

  • 1JEIP, UAR 3573 CNRS, Collège de France, PSL Research University, 11 Place Marcelin Berthelot, 75321 Paris Cedex 05, France
  • 2Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA
  • 3Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
  • 4Center for Computational Mathematics, Flatiron Institute, New York, New York 10010, USA
  • 5Collège de France, PSL University, 11 place Marcelin Berthelot, 75005 Paris, France
  • 6Department of Quantum Matter Physics, University of Geneva, 24 quai Ernest-Ansermet, 1211 Geneva, Switzerland
  • 7CPHT, CNRS, Ecole Polytechnique, IP Paris, F-91128 Palaiseau, France

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Phys. Rev. X 16, 011067 – Published 26 March, 2026

DOI: https://doi.org/10.1103/4ys9-ct98

Abstract

Many-body systems that saturate the quantum bound on chaos are attracting interest across a wide range of fields. Notable examples include the Sachdev-Ye-Kitaev model and its variations, all characterized by some form or randomness and all-to-all couplings. Here, we study many-body quantum chaos in a quantum impurity model showing non-Fermi-liquid physics, the overscreened multichannel SU(N) Kondo model. We exactly compute the low-temperature behavior of the out-of-time order correlator in the limit of large N and large number of channels, K, at a fixed ratio γ=K/N. Because of strong correlations at the impurity site, the spin fractionalizes in auxiliary fermions and bosons. We show that all the degrees of freedom of our theory acquire a Lyapunov exponent that is linear in temperature as T→0, with a prefactor that depends on γ. Remarkably, for N=K, the impurity spin displays maximal chaos, while bosons and fermions only reach half of the maximal Lyapunov exponent. Our results highlight two key features: a nondisordered model that is maximally chaotic due to strong correlations at its boundary, with the maximal chaos appearing in a composite gauge-invariant operator, the impurity spin, and not in the auxiliary single-particle degrees of freedom.

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Popular Summary

In quantum mechanics, information initially encoded in local degrees of freedom is not lost over time but is instead “scrambled” into nonlocal degrees of freedom. While maximal quantum chaos and fast scrambling are typically associated with models featuring random all-to-all interactions, such as the Sachdev-Ye-Kitaev model, we show that randomness is not a fundamental requirement. By exactly computing the low-temperature behavior of the out-of-time-order correlator for the overscreened multichannel SU(N) Kondo model, we demonstrate that a boundary quantum spin strongly coupled to free fermions can saturate the quantum bound on chaos. Our results reveal that while auxiliary single-particle degrees of freedom acquire only half the maximal Lyapunov exponent, the physical impurity spin acts as a fast scrambler. This identification of maximal chaos at a boundary without quenched randomness provides a new perspective for classifying non-Fermi-liquid phases and hints at potential gravity analogs for quantum impurity models.

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Phys. Rev. X 16, 011067– Published 26 March, 2026
  • Received 8 August 2024
  • Revised 19 December 2025
  • Accepted 20 January 2026
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