Universality in the onset of quantum chaos in many-body systems

TL;DR

This paper demonstrates that the onset of quantum chaos in certain many-body systems exhibits universal behavior characterized by specific spectral and fidelity susceptibility features, indicating chaos can arise from arbitrarily small perturbations as system size grows.

Contribution

It reveals universal markers of quantum chaos onset in many-body systems and shows that chaos can emerge from minimal perturbations in the thermodynamic limit.

Findings

Maxima of fidelity susceptibilities scale with inverse level spacing squared.

Spectral function diverges below the Thouless energy near chaos onset.

Small perturbations suffice to induce chaos in large systems.

Abstract

We show that the onset of quantum chaos at infinite temperature in two many-body one-dimensional lattice models, the perturbed spin-1/2 XXZ and Anderson models, is characterized by universal behavior. Specifically, we show that the onset of quantum chaos is marked by maxima of the typical fidelity susceptibilities that scale with the square of the inverse average level spacing, saturating their upper bound, and that the strength of the integrability- or localization-breaking perturbation at these maxima decreases with increasing system size. We also show that the spectral function below the ``Thouless'' energy (in the quantum-chaotic regime) diverges when approaching those maxima. Our results suggest that, in the thermodynamic limit, arbitrarily small integrability- or localization-breaking perturbations result in quantum chaos in the many-body quantum systems studied here.