Topological Dualities from Matchgate Tensor Networks

Explore a comprehensive lecture on topological dualities and matchgate tensor networks presented by Carolin Wille from the University of Cambridge at IPAM's Tensor Networks Workshop. Delve into the fascinating connections between the ground state of the toric code, the two-dimensional class D superconductor, and the partition sum of the two-dimensional Ising model. Examine how these seemingly disparate systems from different areas of physics are linked through remarkable dualities. Investigate the challenges posed by the non-local nature of these connections and discover how matchgate tensor networks offer a unified approach to understanding these complex relationships. Gain insights into long-range entangled topological order, topological band insulators, and classical statistical mechanics as you unravel the intricacies of this groundbreaking research in quantum physics and mathematical modeling.