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

TL;DR

This study uses Pfaffian Monte Carlo to analyze entanglement entropy in RVB quantum spin liquids on triangular and kagome lattices, confirming topological order and quasiparticle statistics consistent with the toric code model.

Contribution

It demonstrates a method to compute entanglement entropy in RVB states without sign problems and confirms the topological nature and quasiparticle statistics of the spin liquids.

Findings

Topological entanglement entropy consistent with ln(2)

Mutual statistics match toric code anyon model

Rules out double semion quasiparticle statistics

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.