Maximal quantum chaos of the critical Fermi surface

Abstract

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 $2\pi k_{B}T/\hslash$, where $T$ is the absolute temperature. We also examine a phenomenological model in which the chaos exponent becomes smaller than the maximal value precisely when quasiparticles are restored.

arXiv commentUpdated with more information on the phenomenological model and other minor corrections and clarifications. Main manuscript 6 pages, SI 9 pages

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