Rényi entanglement entropies in quantum dimer models : from criticality to topological order

Abstract

Thanks to Pfaffian techniques, we study the Rényi entanglement entropies and the entanglement spectrum of large subsystems for two-dimensional Rokhsar-Kivelson wave functions constructed from a dimer model on the triangular lattice. By including a fugacity $t$ on some suitable bonds, one interpolates between the triangular lattice (t=1) and the square lattice (t=0). The wave function is known to be a massive ${\mathbb{Z}}_2$ topological liquid for $t>0$ whereas it is a gapless critical state at t=0. We mainly consider two geometries for the subsystem: that of a semi-infinite cylinder, and the disk-like setup proposed by Kitaev and Preskill [Phys. Rev. Lett. 96, 110404 (2006)]. In the cylinder case, the entropies contain an extensive term -- proportional to the length of the boundary -- and a universal sub-leading constant $s_n(t)$. Fitting these cylinder data (up to a perimeter of L=32 sites) provides $s_n$ with a very high numerical accuracy ($10^{-9}$ at t=1 and $10^{-6}$ at $t=0.5$). In the topological ${\mathbb{Z}}_2$ liquid phase we find $s_n(t>0)=-\ln 2$, independent of the fugacity $t$ and the Rényi parameter $n$. At t=0 we recover a previously known result, $s_n(t=0)=-(1/2)\ln (n)/(n-1)$ for $n<1$ and $s_n(t=0)=-\ln (2)/(n-1)$ for $n>1$. In the disk-like geometry -- designed to get rid of the boundary contributions -- we find an entropy $s_n^{\mathrm{KP}}(t>0)=-\ln 2$ in the whole massive phase whatever $n>0$, in agreement with the result of Flammia {\it et al.} [Phys. Rev. Lett. 103, 261601 (2009)]. Some results for the gapless limit $R_n^{\mathrm{KP}}(t\to 0)$ are discussed.

33 pages, 17 figures, minor corrections

References in corpus (18)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Topological Order and Conformal Quantum Critical Points
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• Topological Entanglement Entropy of a Bose-Hubbard Spin Liquid
• Ground state entanglement and geometric entropy in the Kitaev's model
• Entanglement entropy in fermionic Laughlin states
• Universal entanglement entropy in 2D conformal quantum critical points
• Bipartite entanglement entropy in fractional quantum Hall states
• Interacting classical dimers on the square lattice
• Topological Entanglement Entropy of Z2 Spin liquids and Lattice Laughlin states
• Rényi entropy of a line in two-dimensional Ising models
• Phase transition in the Rényi-Shannon entropy of Luttinger liquids
• Logarithmic terms in entanglement entropies of 2D quantum critical points and Shannon entropies of spin chains
• On bipartite Rokhsar-Kivelson points and Cantor deconfinement
• Quantum criticality, lines of fixed points, and phase separation in doped two-dimensional quantum dimer models
• Universal behavior of a bipartite fidelity at quantum criticality
• Universal Behavior of Entanglement in 2D Quantum Critical Dimer Models
• Boundary Conformal Field Theory and Entanglement Entropy in Two-Dimensional Quantum Lifshitz Critical Point

Cited by in corpus (22)

• Topological and Entanglement Properties of Resonating Valence Bond wavefunctions
• Tensor Networks for Lattice Gauge Theories with continuous groups
• Renyi Entropies for Free Field Theories
• Entanglement scaling in two-dimensional gapless systems
• Shannon-Rényi entropies and participation spectra across 3d $O(3)$ criticality
• Topological transitions from multipartite entanglement with tensor networks: a procedure for sharper and faster characterization
• Entanglement in gapless resonating valence bond states
• Two-cylinder entanglement entropy under a twist
• Entanglement Spectra of the quantum hard-square model: Holographic minimal models
• Scaling of entanglement in $2+1$-dimensional scale-invariant field theories
• Entanglement Entropy in Generalised Quantum Lifshitz Models
• Exact solution of the $2d$ dimer model: Corner free energy, correlation functions and combinatorics
• Many-body Localization Transition in Rokhsar-Kivelson-type wave functions
• Particle partition entanglement of bosonic Luttinger liquids
• Accuracy of topological entanglement entropy on finite cylinders
• Distilling topological entropy from single entanglement measures on projected systems
• Entanglement Entropy at Generalized Rokhsar-Kivelson Points of Quantum Dimer Models
• An efficient Monte Carlo algorithm for the evaluation of Renyi entanglement entropy of a general quantum dimer model at the R-K point
• Entanglement dynamics in monitored Kitaev circuits: loop models, symmetry classification, and quantum Lifshitz scaling
• Universal Renyi mutual information in classical systems: the case of kagome ice
• Symmetrizing the Constraints -- Density Matrix Renormalization Group for Constrained Lattice Models
• Exactly Solvable Topological Phase Transition in a Quantum Dimer Model