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Explore the fundamental concepts of Hilbert space fragmentation and many-body scars in this comprehensive lecture from the ICTP-SAIFR Program on Quantum Many-Body Dynamics. Learn how quantum many-body systems can exhibit violations of thermalization through the phenomenon of Hilbert space fragmentation, where the system's Hilbert space breaks into disconnected sectors that cannot communicate with each other. Discover the theoretical framework behind many-body scars, which are special eigenstates that violate the eigenstate thermalization hypothesis and lead to persistent oscillations in quantum systems. Examine the mathematical foundations of these concepts and their implications for understanding non-ergodic behavior in quantum many-body systems. Gain insights into how these phenomena challenge our understanding of thermalization in isolated quantum systems and their potential applications in quantum information and quantum simulation. This first class in the series provides essential groundwork for understanding advanced topics in quantum many-body dynamics and the mechanisms that prevent systems from reaching thermal equilibrium.
