Matrix Product Operator Algebras in Topological Order

Explore the connection between topological order in two-dimensional systems and fusion categories in this 49-minute conference talk from the Thematic Programme on "Tensor Networks: Mathematical Structures and Novel Algorithms" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into how topological order emerges in PEPS due to specific MPO symmetries of defining tensors, with MPOs identified as fusion categories. Discover an alternative perspective on MPO symmetries as representations of certain algebras, specifically weak Hopf algebras, providing an equivalent language to discuss these symmetries. Gain insights into the mathematical structures underlying tensor networks and their applications in understanding complex quantum systems.