Entanglement Entropy at Generalized Rokhsar-Kivelson Points of Quantum Dimer Models

TL;DR

This study computes the topological entanglement entropy of quantum dimer models at generalized Rokhsar-Kivelson points, confirming topological order and universality across a phase, with detailed analysis of corner effects.

Contribution

It extends the calculation of topological entanglement entropy to generalized RK points and demonstrates its universality across a topologically ordered phase.

Findings

TEE at RK point is approximately 0.693, confirming earlier results

TEE remains universal across a range of parameters within the topological phase

Corner contributions to entanglement entropy are proportional to corner types and counts

Abstract

We study the $n=2$ R\' enyi entanglement entropy of the triangular quantum dimer model via Monte Carlo sampling of Rokhsar-Kivelson(RK)-like ground state wavefunctions. Using the construction proposed by Kitaev and Preskill [Phys. Rev. Lett. 96, 110404 (2006)] and an adaptation of the Monte Carlo algorithm described by Hastings \emph{et al.} [Phys. Rev. Lett. 104, 157201 (2010)], we compute the topological entanglement entropy (TEE) at the RK point $\gamma = (1.001 \pm 0.003) \ln 2$ confirming earlier results. Additionally, we compute the TEE of the ground state of a generalized RK-like Hamiltonian and demonstrate the universality of TEE over a wide range of parameter values within a topologically ordered phase approaching a quantum phase transition. For systems sizes that are accessible numerically, we find that the quantization of TEE depends sensitively on correlations. We characterize corner contributions to the entanglement entropy and show that these are well described by shifts proportional to the number and types of corners in the bipartition.