Maximal quantum chaos of the critical Fermi surface

TL;DR

This paper demonstrates that non-Fermi liquid states with Fermi surfaces in two dimensions exhibit maximal quantum chaos, with Lyapunov exponents reaching the theoretical upper bound at finite temperature.

Contribution

It applies a large N theory and ladder identity to compute chaos in critical Fermi surfaces, revealing maximal Lyapunov exponents in these non-Fermi liquid states.

Findings

Chaos Lyapunov exponent reaches the maximal value of 2πk_B T/ħ.

Maximal chaos occurs in the critical Fermi surface state.

Restoration of quasiparticles reduces the chaos exponent.

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 $2 \pi k_B T/\hbar$, 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.