Open-system eigenstate thermalization in a noninteracting integrable model

Abstract

Significant attention has been devoted to the problem of thermalization of observables in isolated quantum setups by individual eigenstates. Here, we address this issue from an open quantum system perspective, examining an isolated setup where a small system (specifically, a single fermionic level) is coupled to a macroscopic fermionic bath. We argue that in such a model, despite its full integrability, the system observables exhibit thermalization when the system-bath setup resides in a typical eigenstate of its Hamiltonian, a phenomenon known as weak eigenstate thermalization. This thermalization occurs unless it is suppressed by localization due to strong coupling. We further show that following the quench of the system Hamiltonian, the system occupancy typically relaxes to the thermal value corresponding to the new Hamiltonian. Finally, we demonstrate that system thermalization also arises when the system is coupled to a bath that has been initialized in a typical eigenstate of its Hamiltonian. Our findings suggest that nonintegrability is not the sole driver of thermalization, highlighting the need for complementary approaches to fully understand the emergence of statistical mechanics.