Topological Entanglement Rényi Entropy and Reduced Density Matrix Structure

We generalize the topological entanglement entropy to a family of topological Rényi entropies parametrized by a parameter $\alpha$, in an attempt to find new invariants for distinguishing topologically ordered phases. We show that, surprisingly, all topological Rényi entropies are the same, independent of $\alpha$ for all nonchiral topological phases. This independence shows that topologically ordered ground-state wave functions have reduced density matrices with a certain simple structure, and no additional universal information can be extracted from the entanglement spectrum.