Athermality of generalized Gibbs ensembles

Isolated quantum systems evolving unitarily from non-equilibrium initial states generically thermalize [1–7]. This means that, at long times, the reduced density matrix of a finite subsystem embedded in a thermodynamically large system approaches the reduced density matrix of a thermal ensemble, with the temperature uniquely fixed by the energy density of the initial state. As a consequence, although the full system remains at all times in a pure state characterized by zero von Neumann entropy, finite subsystems behave locally as if they were in thermal equilibrium. In this sense, entanglement with the rest of the system effectively acts as a thermal bath for local observables [8–11]. This mechanism provides the modern understanding of thermalization in isolated quantum many-body systems. From a dynamical perspective, one of the most intriguing aspects of quantum integrable models [12] is their failure to thermalize under quantum unitary dynamics. In these systems, the existence of an extensive number of mutually compatible conservation laws strongly suppresses the scrambling of local quantum information, providing a natural mechanism for local memory retention. Importantly, despite the fragile nature of integrability, this behavior persists over long prethermal timescales [13–27] even in experimentally realistic settings [28–30]. For this reason, at long times…