An efficient Monte Carlo algorithm for the evaluation of Renyi entanglement entropy of a general quantum dimer model at the R-K point

TL;DR

This paper introduces a highly efficient Monte Carlo algorithm to evaluate Renyi entanglement entropy in quantum dimer models at the R-K point, enabling analysis at the thermodynamic limit and revealing lattice-dependent entanglement properties.

Contribution

The paper presents a new Monte Carlo method for calculating Renyi entanglement entropy in quantum dimer models at the R-K point, applicable to large systems and different lattice geometries.

Findings

REE scales linearly with system size on both lattices.

Clear topological entanglement entropy of ln(2) on the triangular lattice.

Oscillations and boundary effects observed on the square lattice.

Abstract

A highly efficient and simple to implement Monte Carlo algorithm is proposed for the evaluation of the Renyi entanglement entropy(REE) of quantum dimer model(QDM) at the Rokhsar-Kivelson(R-K) point. It makes possible the evaluation of REE at the R-K point to the thermodynamic limit for a general QDM. We apply the algorithm to QDM on both triangular and square lattice as demonstrations and find the REE on both lattices follow perfect linear scaling in the thermodynamic limit, apart from an even-odd oscillation in the latter case. We also evaluate the topological entanglement entropy(TEE) on both lattices with a subtraction procedure. While the expected TEE of $\ln2$ is clearly demonstrated for QDM on triangular lattice, a strong oscillation of the result is found for QDM on square lattice, which implies the relevance of boundary perturbation in such a critical system.