IQI Weekly Seminar

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 Z_d quantum double models with local fields and Ising-like terms. In addition, we identify ribbons in the abelian phase of Kitaev's honeycomb model. We further identify the topologically encoded qubit in the quantum compass model, and show that despite this qubit, the model does not support topological order. 

 

Joint work with Jacob Bridgeman and Steve Flammia