Ergodicity Breaking in Quantum Many-Body Systems

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.

Introduction
Outline
Isolated systems
Local thermal equilibrium
Eigenstate expectations
What can break ergodicity
Thermalization in classical systems
Relative Scales
Isolated Quantum Systems
Purity of the State
Eulers Formula
Boundary terms
Onsite terms
Anderson localized systems
Questions
Problems
Quantum phase transition
Numerical studies
Phenomenology
Example