Generalized string-net models: A thorough exposition

Understand

We describe how to construct generalized string-net models, a class of exactly solvable lattice models that realize a large family of 2D topologically ordered phases of matter.

• The ground states of these models can be thought of as superpositions of different "string-net configurations", where each string-net configuration is a trivalent graph with labeled edges, drawn in the $xy$ plane.
• What makes this construction more general than the original string-net construction is that, unlike the original construction, tetrahedral reflection symmetry is not assumed, nor is it assumed that the ground state wave function $\Phi$ is "isotropic": i.e.
• in the generalized setup, two string-net configurations $X_1, X_2$ that can be continuously deformed into one another can have different ground state amplitudes, $\Phi(X_1) \neq \Phi(X_2)$.