Defects and Duality on the Lattice - Tensor Networks in Lattice Models

Explore a comprehensive lecture on lattice models, tensor networks, and topological defects in this talk by Paul Fendley at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the unified framework of lattice models, examining how quantum Hamiltonians and 2D classical transfer matrices can be expressed using algebras, particularly the Temperley-Lieb algebra. Discover the application of fusion categories in analyzing these models and learn how tensor networks provide a natural language for describing these results. Investigate the construction of lattice topological defects that generate symmetries, generalizing the Kramers-Wannier duality of Ising and Potts models. Understand how these "non-invertible" symmetries enable exact computations on the lattice, including g-factors of boundary CFT, critical exponents, and the spectrum of low-lying states. Gain insights into the application of these concepts to the Ryberg-blockade ladder, bridging theoretical foundations with practical implementations in quantum systems.