Classical vertex model dualities in a family of 2D frustrated quantum antiferromagnets

Abstract

We study a general class of easy-axis spin models on a lattice of corner sharing even-sided polygons with all-to-all interactions within a plaquette. The low energy description corresponds to a quantum dimer model on a dual lattice of even coordination number with a multi dimer constraint. At an appropriately constructed frustration-free Rokhsar-Kivelson (RK) point, the ground state wavefunction can be exactly mapped onto a classical vertex model on the dual lattice. When the dual lattice is bipartite, the vertex models are bonded and are self dual under Wegner's duality, with the self dual point corresponding to the RK point of the original multi-dimer model. We argue that the self dual point is a critical point based on known exact solutions to some of the vertex models. When the dual lattice is non-bipartite, the vertex model is arrowed, and we use numerical methods to argue that there is no phase transition as a function of the vertex weights. Motivated by these wavefunction dualities, we construct two other distinct families of frustration-free Hamiltonians whose ground states can be mapped onto these vertex models. Many of these RK Hamiltonians provably host ${\mathbb{Z}}_2$ topologically ordered phases.

arXiv comment30 pages, 13 figures

References in corpus (19)

• Fault-tolerant quantum computation by anyons
• An RVB phase in the triangular lattice quantum dimer model
• Topological Order and Conformal Quantum Critical Points
• Fractionalization in an Easy-axis Kagome Antiferromagnet
• Quantum dimer model on the kagome lattice: solvable dimer liquid and Ising gauge theory
• Prediction of Toric Code Topological Order from Rydberg Blockade
• Relaxation time for a dimer covering with height representation
• Classical dimers on the triangular lattice
• From classical to quantum dynamics at Rokhsar-Kivelson points
• Microscopic models for fractionalized phases in strongly correlated systems
• The "Square Kagome" Quantum Antiferromagnet and the Eight Vertex Model
• Numerical study of a transition between Z2 topologically ordered phases
• Theory of d-density wave viewed from a vertex model and its implications
• Numerical study of fractionalization in an Easy-axis Kagome antiferromagnet
• Comment on "Spin Transport properties of the quantum one-dimensional non-linear sigma model"
• Exact Spin Liquid Ground States of the Quantum Dimer Model on the Square and Honeycomb Lattices
• Conformal invariance studies of the Baxter-Wu model and a related site-colouring problem
• Quantum three-coloring dimer model and the disruptive effect of quantum glassiness on its line of critical points
• Critical properties of the Hintermann-Merlini model

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• Classical fully-packed loop model with attractive interactions on the square lattice
• Breakdown of the thermodynamic limit in quantum spin and dimer models
• A fermionic path integral for exact enumeration of polygons on the simple cubic lattice
• Exactly Solvable Topological Phase Transition in a Quantum Dimer Model