Quantum chaos on a critical Fermi surface

TL;DR

This paper investigates quantum chaos in a critical Fermi surface with no quasiparticles, revealing universal relationships between chaos parameters and thermal diffusivity in a strongly interacting fermionic system.

Contribution

It computes chaos parameters like Lyapunov rate and butterfly velocity for a non-quasiparticle critical Fermi surface coupled to a gauge field, establishing their universal relation to thermal diffusivity.

Findings

Lyapunov rate and butterfly velocity are computed for the system.

Thermal diffusivity is universally related to chaos parameters.

The relationship is independent of system-specific parameters.

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.