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

Cited by in corpus (17)

• Quantum quench of the Sachdev-Ye-Kitaev Model
• Thermal diffusivity and chaos in metals without quasiparticles
• Scrambling in Random Unitary Circuits: Exact Results
• An upper bound on transport
• Diffusion and Chaos from near AdS${}_2$ horizons
• Complete random matrix classification of SYK models with $\mathcal{N}=0$, $1$ and $2$ supersymmetry
• Tunable Quantum Chaos in the Sachdev-Ye-Kitaev Model Coupled to a Thermal Bath
• Scrambling and Complexity in Phase Space
• Diffusion in higher dimensional SYK model with complex fermions
• Universal Bounds on Transport in Holographic Systems with Broken Translations
• Thermalization and Possible Signatures of Quantum Chaos in Complex Crystalline Materials
• A lower bound to the thermal diffusivity of insulators
• Scrambling versus relaxation in Fermi and non-Fermi liquids
• Holographic Butterfly Effect and Diffusion in Quantum Critical Region
• Interferometric-Spectroscopy With Quantum-Light; Revealing Out-of-Time-Ordering Correlators
• Constraints on hydrodynamics from many-body quantum chaos
• Quantum many-body physics from a gravitational lens