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

Abstract

On the triangular and kagome lattices, short-ranged resonating valence bond (RVB) wave functions can be sampled without the sign problem using a recently-developed Pfaffian Monte Carlo scheme. In this paper, we study the Renyi entanglement entropy in these wave functions using a replica-trick method. Using various spatial bipartitions, including the Levin-Wen construction, our finite-size scaled Renyi entropy gives a topological contribution consistent with $\gamma =\text{ln}(2)$, as expected for a gapped ${\mathbb{Z}}_2$ quantum spin liquid. We prove that the mutual statistics are consistent with the toric code anyon model and rule out any other quasiparticle statistics such as the double semion model.

4 pages, 10 pages supplemental material, references updated, text passage rewritten for clarity

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• Mean-field theory of interacting triplons in a two-dimensional valence-bond solid: stability and properties of many-triplon states
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• Entanglement studies of resonating valence bonds on the frustrated square lattice