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Explore the fundamental concepts of emergent phenomena in strongly correlated quantum systems through this comprehensive lecture from the II School on Emergent Phenomena in Non-Equilibrium Quantum Many-Body Systems. Delve into the complex interactions between particles in quantum many-body systems where conventional single-particle descriptions break down and collective behaviors emerge. Learn how strong correlations between electrons and other quantum particles give rise to unexpected physical properties and phases of matter that cannot be understood from the properties of individual components alone. Examine theoretical frameworks and computational approaches used to study these systems, including advanced techniques for analyzing quantum phase transitions, exotic ground states, and non-trivial ordering phenomena. Discover how emergent properties manifest in real materials and experimental systems, with particular attention to high-temperature superconductors, quantum magnets, and other strongly correlated electron systems. Gain insights into the mathematical tools and physical intuition needed to understand how macroscopic quantum phenomena arise from microscopic interactions, setting the foundation for advanced studies in condensed matter physics and quantum many-body theory.
