Quantum chaos on a critical Fermi surface

Abstract

We compute parameters characterizing many-body quantum chaos for a critical Fermi surface without quasiparticle excitations. We examine a theory of $N$ species of fermions at non-zero density coupled to a $U(1)$ gauge field in two spatial dimensions, and determine the Lyapunov rate and the butterfly velocity in an extended random-phase approximation. The thermal diffusivity is found to be universally related to these chaos parameters i.e. the relationship is independent of $N$, the gauge coupling constant, the Fermi velocity, the Fermi surface curvature, and high energy details.

22 pages, 5 figures, some signs and typos fixed, results unchanged. Added comment about cancellation of "classical" processes

References in corpus (7)

• Theory of universal incoherent metallic transport
• Low energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions
• Slow scrambling in disordered quantum systems
• Memory matrix theory of magnetotransport in strange metals
• Charge diffusion and the butterfly effect in striped holographic matter
• Transport Properties of a spinon Fermi surface coupled to a U(1) gauge field
• A controlled expansion for certain non-Fermi liquid metals

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