Topological Symmetry and Duality in Quantum Lattice Models - Lecture 1

Explore a comprehensive lecture on topological symmetry and duality in quantum lattice models presented by Clément Delcamp at the Institut des Hautes Etudes Scientifiques (IHES). Delve into a modern perspective on symmetry in quantum theories, focusing on the topological invariance of symmetry operators within correlation functions. Discover how this viewpoint enables a calculus of topological defects with strong category-theoretic elements, leveraging methods from topological quantum field theory. Examine finite symmetries in the context of one-dimensional quantum lattice models, learning about a framework for systematically investigating lattice Hamiltonians, elucidating symmetry operators, and defining duality/gauging transformations. Gain insights into the classification of gapped symmetric phases for generalized symmetry and the construction of corresponding order/disorder parameters. Benefit from explicit treatments of familiar physical systems from condensed matter theory, shedding light on celebrated results and offering resolutions to certain open problems. Conclude with brief discussions on generalizations to higher dimensions and implications for numerical simulations in this 1 hour and 50 minutes long lecture.