Probing chaos in the spherical p-spin glass model

TL;DR

This paper investigates chaos in a quantum p-spin glass model, revealing that maximal chaos correlates with fastest relaxation and landscape complexity, and suggests ergodicity breaking at low energies.

Contribution

It provides a detailed analysis of chaos indicators in the quantum p-spin glass model and links chaos to relaxation dynamics and energy landscape features.

Findings

Chaos peaks at specific initial energies.

Maximal chaos aligns with fastest relaxation.

Hints of ergodicity breaking at low energies.

Abstract

We study the dynamics of a quantum $p$-spin glass model starting from initial states defined in microcanonical shells, in a classical regime. We compute different chaos estimators, such as the Lyapunov exponent and the Kolmogorov-Sinai entropy, and find a marked maximum as a function of the energy of the initial state. By studying the relaxation dynamics and the properties of the energy landscape we show that the maximal chaos emerges in correspondence with the fastest spin relaxation and the maximum complexity, thus suggesting a qualitative picture where chaos emerges as the trajectories are scattered over the exponentially many saddles of the underlying landscape. We also observe hints of ergodicity breaking at low energies, indicated by the correlation function and a maximum of the fidelity susceptibility.