Probing semi-classical chaos in the spherical $p$-spin glass model

Lorenzo Correale, Anatoli Polkovnikov, Marco Schirò, Alessandro Silva

Published 2023-03-27Version 1

We study semiclassically the dynamics of a quantum $p$-spin glass model starting from initial states defined in microcanonical shells. 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.