Topological Symmetry and Duality in Quantum Lattice Models - Lecture 2

Explore the second lecture in a four-part series on topological symmetry and duality in quantum lattice models. Delve into a modern perspective on symmetry in quantum theories, focusing on the topological invariance of symmetry operators within correlation functions. Examine generalised notions of symmetry and the calculus of topological defects, drawing connections to category theory and topological quantum field theory. Investigate finite symmetries in one-dimensional quantum lattice models, learning how to systematically analyze lattice Hamiltonians, identify symmetry operators, and define duality/gauging transformations. Discover methods for computing the mapping of topological sectors through these transformations. Gain insights into the classification of gapped symmetric phases for generalised symmetry and the construction of corresponding order/disorder parameters. Explore explicit treatments of familiar physical systems from condensed matter theory, shedding light on celebrated results and offering resolutions to certain open problems. If time permits, briefly touch upon generalisations to higher dimensions and implications for numerical simulations.