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2019

Chaos in the butterfly cone

Mezei, Márk, Sárosi, Gábor

Understand

A simple probe of chaos and operator growth in many-body quantum systems is the out of time ordered four point function.

In a large class of local systems, the effects of chaos in this correlator build up exponentially fast inside the so called butterfly cone.
It has been previously observed that the growth of these effects is organized along rays and can be characterized by a velocity dependent Lyapunov exponent, $\lambda({\bf v})$.
We show that this exponent is bounded inside the butterfly cone as $\lambda({\bf v})\leq 2\pi T(1-|{\bf v}|/v_B)$, where $T$ is the temperature and $v_B$ is the butterfly speed.