Department of Physics, Renmin University of China, Beijing 100872, People's Republic of China.
J Phys Condens Matter. 2014 Jan 22;26(3):035601. doi: 10.1088/0953-8984/26/3/035601. Epub 2013 Dec 12.
A highly efficient and simple-to-implement Monte Carlo algorithm is proposed for the evaluation of the Rényi entanglement entropy (REE) of the quantum dimer model (QDM) at the Rokhsar-Kivelson (RK) point. It makes possible the evaluation of REE at the RK point to the thermodynamic limit for a general QDM. We apply the algorithm to a QDM defined on the triangular and the square lattice in two dimensions and the simple and the face centered cubic (fcc) lattice in three dimensions. We find the REE on all these lattices follows perfect linear scaling in the thermodynamic limit, apart from an even-odd oscillation in the case of the square lattice. We also evaluate the topological entanglement entropy (TEE) with both a subtraction and an extrapolation procedure. We find the QDMs on both the triangular and the fcc lattice exhibit robust Z2 topological order. The expected TEE of ln2 is clearly demonstrated in both cases. Our large scale simulation also proves the recently proposed extrapolation procedure in cylindrical geometry to be a highly reliable way to extract the TEE of a topologically ordered system.
提出了一种高效且易于实现的蒙特卡罗算法，用于评估量子二聚体模型（QDM）在 Rokhsar-Kivelson（RK）点的 Renyi 纠缠熵（REE）。它使得对一般 QDM 的 RK 点的 REE 能够评估到热力学极限。我们将该算法应用于二维的三角形和正方形晶格以及三维的简单立方和面心立方晶格上的 QDM。我们发现所有这些晶格上的 REE 在热力学极限下都呈现出完美的线性标度，除了正方形晶格的奇偶振荡之外。我们还使用减法和外推程序评估了拓扑纠缠熵（TEE）。我们发现，三角形和面心立方晶格上的 QDM 都表现出稳健的 Z2 拓扑序。在这两种情况下，ln2 的预期 TEE 都得到了清晰的证明。我们的大规模模拟也证明了最近提出的圆柱几何中的外推程序是一种从拓扑有序系统中提取 TEE 的高度可靠方法。
