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Explore the fundamental concept of ergodicity breaking in quantum many-body systems through this comprehensive colloquium talk. Delve into two key mechanisms: many-body localization in isolated systems with quenched randomness, and the competition between quantum dynamics and measurements. Examine theoretical approaches from the perspective of many-body Hilbert/Fock spaces, uncovering necessary conditions for non-ergodic behavior and the nature of phase transitions between ergodic and localized states. Investigate how non-ergodicity manifests in quantum entanglement dynamics, focusing on a novel entanglement phase transition induced by measurements and its potential relationship to many-body localization. Gain insights into the emergence of thermodynamics from microscopic descriptions of complex systems and understand scenarios that fall outside conventional statistical mechanics paradigms.
