Detecting Topological Order with Ribbon Operators

Understand

We introduce a numerical method for identifying topological order in two-dimensional models based on one-dimensional bulk operators.

• The idea is to identify approximate symmetries supported on thin strips through the bulk that behave as string operators associated to an anyon model.
• We can express these ribbon operators in matrix product form and define a cost function that allows us to efficiently optimize over this ansatz class.
• We test this method on spin models with abelian topological order by finding ribbon operators for $\mathbb{Z}_d$ quantum double models with local fields and Ising-like terms.