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On the triangular and kagome lattices, short-ranged resonating valence bond(RVB) wave functions can be sampled without the sign problem using arecently-developed Pfaffian Monte Carlo scheme. In this paper, we study theRenyi entanglement entropy in these wave functions using a replica-trickmethod. Using various spatial bipartitions, including the Levin-Wenconstruction, our finite-size scaled Renyi entropy gives a topologicalcontribution consistent with $\gamma = \text{ln}(2)$, as expected for a gapped$\mathbb{Z}_{2}$ quantum spin liquid. We prove that the mutual statistics areconsistent with the toric code anyon model and rule out any other quasiparticlestatistics such as the double semion model.

Entanglement Entropy and Topological Order in Resonating Valence-Bond Quantum Spin Liquids