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Explore tensor network based methods in this comprehensive physics lecture from the Boulder Summer School 2025, where you'll learn fundamental concepts and applications of tensor networks in quantum many-body systems. Discover how tensor network states provide efficient representations of quantum states, understand the mathematical framework underlying matrix product states (MPS) and projected entangled pair states (PEPS), and examine computational algorithms for simulating quantum systems. Master the principles of entanglement scaling, area laws, and how tensor networks capture the essential physics of strongly correlated quantum matter. Gain insights into practical implementation techniques, numerical methods for optimization, and the role of tensor networks in quantum information theory and condensed matter physics through detailed mathematical derivations and illustrative examples presented by an expert in the field.
