Fast Scrambling at the Boundary

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>S</a:mi> <a:mi>U</a:mi> <a:mo stretchy="false">(</a:mo> <a:mi>N</a:mi> <a:mo stretchy="false">)</a:mo> </a:math> Kondo model. We exactly compute the low-temperature behavior of the out-of-time order correlator in the limit of large <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>N</e:mi> </e:math> and large number of channels, <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>K</g:mi> </g:math> , at a fixed ratio <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>γ</i:mi> <i:mo>=</i:mo> <i:mi>K</i:mi> <i:mo>/</i:mo> <i:mi>N</i:mi> </i:math> . 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 <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi>T</k:mi> <k:mo stretchy="false">→</k:mo> <k:mn>0</k:mn> </k:math> , with a prefactor that depends on <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:mi>γ</n:mi> </n:math> . Remarkably, for <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:mi>N</p:mi> <p:mo>=</p:mo> <p:mi>K</p:mi> </p:math> , 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.