Generalized string-net models: A thorough exposition

We describe how to construct generalized string-net models, a class of exactly solvable lattice models that realize large family 2D topologically ordered phases matter. The ground states these can be thought as superpositions different "string-net configurations", where each configuration is trivalent graph with labeled edges, drawn in the $xy$ plane. What makes this construction more general than original that, unlike construction, tetrahedral reflection symmetry not assumed, nor it assumed state wave function $\Phi$ "isotropic": i.e. setup, two configurations $X_1, X_2$ continuously deformed into one another have amplitudes, $\Phi(X_1) \neq \Phi(X_2)$. As result, topological are inaccessible construction. In paper, we provide detailed discussion functions, Hamiltonians, and minimal self-consistency conditions for what exists previous literature. also show string operators create anyon excitations compute braiding statistics excitations. Finally, derive necessary sufficient isotropic functions on plane or sphere -- property may useful some applications.