Modular transformations and topological orders in two dimensions

Understand

The string-net approach by Levin and Wen and the local unitary transformation approach by Chen, Gu and Wen provided ways to systematically label non-chiral topological orders in 2D.

• In those approaches, different topologically ordered many-body wave functions were characterized by different fixed-point tensors.
• Though extremely powerful, the resulting fixed-point tensors were mathematical abstractions and thus lacked a physical interpretation.
• As a result it was hard to judge if two different fixed-point tensors described the same quantum phase or not.