Maximal Quantum Chaos of the Critical Fermi Surface.

We investigate the many-body quantum chaos of non-Fermi liquid states with Fermi surfaces in two spatial dimensions by computing their out-of-time-order correlation functions. Using a recently proposed large N theory for the critical Fermi surface, and the ladder identity of Gu and Kitaev, we show that the chaos Lyapunov exponent takes the maximal value of 2πk_{B}T/ℏ, where T is the absolute temperature. We also examine a phenomenological model that can be continuously tuned between a non-Fermi liquid without quasiparticles and a Fermi liquid with quasiparticles. We find that the Lyapunov exponent becomes smaller than the maximal value precisely when quasiparticles are restored.