Strong and weak thermalization of infinite non-integrable quantum systems

TL;DR

This paper reveals that non-integrable quantum systems exhibit two distinct thermalization behaviors, strong and weak, with some states showing no thermalization within accessible simulation times, highlighting a richer phenomenology than classical systems.

Contribution

The study introduces a new numerical technique to distinguish between strong and weak thermalization regimes in quantum systems, uncovering a third non-thermalizing class.

Findings

Identification of strong and weak thermalization regimes in quantum systems

Discovery of states that do not thermalize within simulated time scales

Introduction of a new numerical method for analyzing quantum thermalization

Abstract

When a non-integrable system evolves out of equilibrium for a long time, local observables are expected to attain stationary expectation values, independent of the details of the initial state. However, intriguing experimental results with ultracold gases have shown no thermalization in non-integrable settings, triggering an intense theoretical effort to decide the question. Here we show that the phenomenology of thermalization in a quantum system is much richer than its classical counterpart. Using a new numerical technique, we identify two distinct thermalization regimes, strong and weak, occurring for different initial states. Strong thermalization, intrinsically quantum, happens when instantaneous local expectation values converge to the thermal ones. Weak thermalization, well-known in classical systems, happens when local expectation values converge to the thermal ones only after time averaging. Remarkably, we find a third group of states showing no thermalization, neither strong nor weak, to the time scales one can reliably simulate.