Observation of prethermalization in weakly nonintegrable unitary maps

TL;DR

This paper studies prethermalization in weakly nonintegrable quantum systems by analyzing the Lyapunov exponent dynamics, revealing long-lived prethermal states and their eventual convergence to thermal values.

Contribution

It introduces a novel approach using the largest Lyapunov exponent to characterize prethermalization and thermalization timescales in near-integrable quantum systems.

Findings

Identification of long-lived prethermalization plateaus.

Demonstration that Lyapunov exponents converge to thermal values over time.

Establishment of a new timescale for thermalization near integrability.

Abstract

We investigate prethermalization by studying the statistical properties of the time-dependent largest Lyapunov exponent $\Lambda(t)$ for unitary-circuit maps upon approaching integrability. We follow the evolution of trajectories for different initial conditions and compute the mean $\mu(t)$ and standard deviation $\sigma(t)$ of $\Lambda(t)$. Thermalization implies a temporal decay $\sigma \sim t^{-1/2}$ at a converged finite value of $\mu$. We report prethermalization plateaus that persist for long times where both $\mu$ and $\sigma$ appear to have converged to finite values, seemingly implying differing saturated Lyapunov exponent values for different trajectories. The lifetime of such plateaus furnishes a novel time scale characterizing the thermalization dynamics of many-body systems close to integrability. We also find that the plateaus converge to their respective thermal values for long enough times.