Renyi entropies for classical string-net models

Abstract

In quantum mechanics, string-net condensed states---a family of prototypical states exhibiting nontrivial topological order---can be classified via their long-range entanglement properties, in particular, topological corrections to the prevalent area law of the entanglement entropy. Here we consider classical analogs of such string-net models whose partition function is given by an equal-weight superposition of classical string-net configurations. Our analysis of the Shannon and Renyi entropies for a bipartition of a given system reveals that the prevalent volume law for these classical entropies is augmented by subleading topological corrections that are intimately linked to the anyonic theories underlying the construction of the classical models. We determine the universal values of these topological corrections for a number of underlying anyonic theories including SU(2)${}_{k}$, SU${(N)}_{1}$, and SU${(N)}_{2}$ theories.