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

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.

11 pages+2 pages sup. mat., 11 Figures. Same text as published version

References in corpus (27)

• Non-Abelian Anyons and Topological Quantum Computation
• Area laws for the entanglement entropy - a review
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• String-net condensation: A physical mechanism for topological phases
• An RVB phase in the triangular lattice quantum dimer model
• Identifying Topological Order by Entanglement Entropy
• Violation of the entropic area law for Fermions
• Measuring Renyi Entanglement Entropy with Quantum Monte Carlo
• Quasi-particle Statistics and Braiding from Ground State Entanglement
• Short-ranged RVB physics, quantum dimer models and Ising gauge theories
• Topological Entanglement Entropy of a Bose-Hubbard Spin Liquid
• Ground state entanglement and geometric entropy in the Kitaev's model
• Topological Entanglement Renyi Entropy and Reduced Density Matrix Structure
• Topological Entanglement Entropy in Chern-Simons Theories and Quantum Hall Fluids
• Shannon and entanglement entropies of one- and two-dimensional critical wave functions
• Topological Entanglement Entropy in the Quantum Dimer Model on the Triangular Lattice
• Classical dimers on the triangular lattice
• Universal entanglement entropy in 2D conformal quantum critical points
• From quantum mechanics to classical statistical physics: generalized Rokhsar-Kivelson Hamiltonians and the "Stochastic Matrix Form" decomposition
• Phase transition in the Rényi-Shannon entropy of Luttinger liquids
• Zero-Temperature Properties of the Quantum Dimer Model on the Triangular Lattice
• Scaling of Entanglement Entropy at 2D quantum Lifshitz fixed points and topological fluids
• Entanglement entropy of integer Quantum Hall states in polygonal domains
• Rényi entanglement entropies in quantum dimer models : from criticality to topological order
• Criticality of a classical dimer model on the triangular lattice
• Loop condensation in the triangular lattice quantum dimer model

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• Symmetrizing the Constraints -- Density Matrix Renormalization Group for Constrained Lattice Models
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