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.

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

References in corpus (3)

• Low energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions
• Quantum chaos on a critical Fermi surface
• Large $N$ theory of critical Fermi surfaces

Cited by in corpus (2)

• Quantum chaos and phase transition in the Yukawa-SYK model
• Strange metal phase of disordered magic-angle twisted bilayer graphene at low temperatures: from flatbands to weakly coupled Sachdev-Ye-Kitaev bundles