Topological order

Two-dimensional topological order has caught much attention in connection to topological phases of matter and topological quantum computation, in particular. It is known that tensor networks are useful tools to study mathematical structures appearing in these topics. We present recent understanding of them from a viewpoint of operator algebras. No knowledge on operator algebras are assumed.

Tensor networks help describe the structures underlying two-dimensional topological phases and topological quantum computation. This talk develops an operator-algebra perspective on those connections and presents recent mathematical understanding of topological order. The introduction is designed to be accessible without prior training in operator algebras.

…interactions and the classification of topological order from an operator-algebraic perspective in mathematical physics.