Topological Symmetry and Duality in Quantum Lattice Models - Lecture 4

Explore an advanced 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. Examine the calculus of topological defects and its category-theoretic aspects, drawing from established methods in topological quantum field theory. Investigate the application of this program to one-dimensional quantum lattice models, with emphasis on finite symmetries. Learn about a framework for systematically studying lattice Hamiltonians, uncovering symmetry operators, defining duality and gauging transformations, and computing topological sector mappings. Gain insights into the classification of gapped symmetric phases for generalized symmetry and the construction of corresponding order and disorder parameters. Benefit from explicit treatments of familiar physical systems from condensed matter theory, shedding light on celebrated results and addressing open problems. Conclude with brief discussions on higher-dimensional generalizations and implications for numerical simulations in this comprehensive 1 hour and 56 minutes lecture.