Strong and Weak Thermalization of Infinite Nonintegrable Quantum Systems

TLDR

Nonintegrable quantum systems are expected to reach stationary local observables after long evolution, yet the mechanisms of their thermalization remain poorly understood. Using a novel numerical method, the authors distinguish strong and weak thermalization regimes depending on the initial state. They find that strong thermalization occurs when local observables instantly match thermal values, weak thermalization requires time averaging, and a third class of states shows no thermalization on accessible timescales.

Abstract

When a nonintegrable system evolves out of equilibrium for a long time, local observables are in general expected to attain stationary expectation values, independent of the details of the initial state. But the thermalization of a closed quantum system is not yet well understood. Here we show that it presents indeed a much richer phenomenology than its classical counterpart. Using a new numerical technique, we identify two distinct 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, shows convergence to thermal values 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.