Quantum many-body scars and weak breaking of ergodicity

Thermalization is the inevitable fate of many complex quantum systems, whose dynamics allow them to fully explore the vast configuration space regardless of the initial state-the behaviour known as quantum ergodicity. In a quest for experimental realizations of coherent long-time dynamics, efforts have focused on ergodicity-breaking mechanisms, such as integrability and localization. The recent discovery of persistent revivals in quantum simulators based on Rydberg atoms have pointed to the existence of a new type of behaviour where the system rapidly relaxes for most initial conditions, while certain initial states give rise to non-ergodic dynamics. This collective effect has been named 'quantum many-body scarring' by analogy with a related form of weak ergodicity breaking that occurs for a single particle inside a stadium billiard potential. In this Review, we provide a pedagogical introduction to quantum many-body scars and highlight the emerging connections with the semiclassical quantization of many-body systems. We discuss the relation between scars and more general routes towards weak violations of ergodicity due to embedded algebras and non-thermal eigenstates, and highlight possible applications of scars in quantum technology. Most large quantum systems are ergodic, meaning that over time they forget their initial conditions and thermalize. This article reviews our understanding of seemingly ergodic systems that in fact have some long-lived, non-thermal states.