Generalized Symmetries on the Lattice - A Tensor Network Point of View

Explore generalized symmetries in quantum many-body systems through the lens of tensor networks in this comprehensive lecture by Frank Verstraete. Delve into the revolutionary developments in symmetry theory that extend far beyond traditional particle and condensed matter physics paradigms, including higher-form, non-invertible, and subsystem symmetries. Learn how these advanced symmetry concepts provide powerful new frameworks for understanding and classifying quantum phases of matter, particularly those that fall outside conventional classification schemes. Discover the tensor network approach to analyzing these symmetries on lattice systems, gaining insights into how microscopic symmetries manifest in highly nontrivial ways at low energies. Examine the connections between generalized symmetries and exotic quantum phases such as symmetry-protected topological states, and understand how these concepts reshape our comprehension of quantum entanglement, conservation laws, and hydrodynamics in interacting systems. This lecture forms part of a broader program on generalized symmetries and anomalies in quantum phases of matter, designed to provide both conceptual clarity for early-career researchers and cutting-edge insights for the broader physics community working at the forefront of quantum many-body theory.