Effective Quantum Dimer Model for the Kagome Heisenberg Antiferromagnet: Nearby Quantum Critical Point and Hidden Degeneracy

Abstract

The low-energy singlet dynamics of the Quantum Heisenberg Antiferromagnet on the Kagome lattice is described by a quantitative Quantum Dimer Model. Using advanced numerical tools, the latter is shown to exhibit Valence Bond Crystal order with a large 36-site unit cell and hidden degeneracy between even and odd parities. Evidences are given that this groundstate lies in the vicinity of a ${\mathbb{Z}}_2$ dimer liquid region separated by a Quantum Critical Point. Implications regarding numerical analysis and experiments are discussed.

4 pages, 4 figures, deep revision of manuscript including new data, revised figures, new Fig. 2(c) and new references

References in corpus (13)

• Quantum magnetism in the paratacamite family: towards an ideal kagome lattice
• Properties of an algebraic spin liquid on the kagome lattice
• 17O NMR study of the intrinsic magnetic susceptibility and spin dynamics of the quantum kagome antiferromagnet ZnCu3(OH)6Cl2
• Ground State of the Kagome Lattice Heisenberg Antiferromagnet
• Dzyaloshinsky-Moriya Anisotropy in the Spin-1/2 Kagomé Compound ZnCu${}_3$(OH)${}_6$Cl${}_2$
• Plaquette valence bond solid in the frustrated Heisenberg quantum antiferromagnet on the square lattice
• Intrinsic relation between ground-state fidelity and the characterization of a quantum phase transition
• Global phase diagrams of frustrated quantum antiferromagnets in two dimensions: doubled Chern-Simons theory
• Low energy excitations of the kagome antiferromagnet and the spin gap issue
• Optical Kagome lattice for ultra-cold atoms with nearest neighbor interactions
• A Generalized Quantum Dimer Model Applied to the Frustrated Heisenberg Model on the Square Lattice: Emergence of a Mixed Columnar-Plaquette Phase
• Crystallization of the resonating valence bond liquid as vortex condensation
• Magnetic field-induced transition in a quantum magnet described by the Quantum Dimer Model

Cited by in corpus (66)

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• Studying Two Dimensional Systems With the Density Matrix Renormalization Group
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• Controlling frustrated liquids and solids with an applied field in a kagome Heisenberg antiferromagnet
• Projected wave function study of Z2 spin liquids on the kagome lattice for the spin-1/2 quantum Heisenberg antiferromagnet
• Gapped spin liquid with ${\mathbb{Z}}_2$-topological order for kagome Heisenberg model
• Topological and Entanglement Properties of Resonating Valence Bond wavefunctions
• Vanishing spin gap in a competing spin-liquid phase in the kagome Heisenberg antiferromagnet
• Ground-State Energy and Spin Gap of Spin-1/2 Kagome Heisenberg Antiferromagnetic Clusters: Large Scale Exact Diagonalization Results
• Functional renormalization group for the anisotropic triangular antiferromagnet
• Magnetic order and paramagnetic phases in the quantum J1-J2-J3 honeycomb model
• The $S=1/2$ Kagome Heisenberg Antiferromagnet Revisited
• The Heisenberg antiferromagnet on the kagome lattice with arbitrary spin: A high-order coupled cluster treatment
• Valence-bond crystal in the extended kagome spin-1/2 quantum Heisenberg antiferromagnet: A variational Monte Carlo approach
• Vison states and confinement transitions of Z2 spin liquids on the kagome lattice
• Finite-size scaling and boundary effects in two-dimensional valence-bond-solids
• Sweeping cluster algorithm for quantum spin systems with strong geometric restrictions
• Simplex Z_2 spin liquids on the Kagome lattice with Entangled Pair States: spinon and vison coherence lengths, topological entropy and gapless edge modes
• Frustrated magnetism and resonating valence bond physics in two-dimensional kagome-like magnets
• Quantum spin liquids in the absence of spin-rotation symmetry: application to Herbertsmithite
• Generalized Hardcore Dimer Models approach to low-energy Heisenberg frustrated antiferromagnets: general properties and application to the kagome antiferromagnet
• Valence-bond crystals in the kagome spin-1/2 Heisenberg antiferromagnet: a symmetry classification and projected wave function study
• Detection of Symmetry Enriched Topological Phases
• Symmetry Breaking on the Three-Dimensional Hyperkagome Lattice of Na_4Ir_3O_8
• Global scheme of sweeping cluster algorithm to sample among topological sectors
• Widely existing mixed phase structure of quantum dimer model on square lattice
• p6 - Chiral Resonating Valence Bonds in the Kagome Antiferromagnet
• Spin-1/2 Heisenberg antiferromagnet on an anisotropic kagome lattice
• Phase diagram of the 1/3-filled extended Hubbard model on the Kagome lattice
• From the $SU(2)$ Quantum Link Model on the Honeycomb Lattice to the Quantum Dimer Model on the Kagomé Lattice: Phase Transition and Fractionalized Flux Strings
• Variational study of the ground state and spin dynamics of the spin-$\frac{1}{2}$ Kagome antiferromagnetic Heisenberg model and its implication on Hebertsmithite ZnCu${}_3$(OH)${}_6$Cl${}_2$
• Quantum Electrodynamics in 2+1 Dimensions as the Organizing Principle of a Triangular Lattice Antiferromagnet
• Resonating valence bond physics is not always governed by the shortest tunneling loops
• Thermodynamics and phase transitions for the Heisenberg model on the pinwheel distorted kagome lattice
• Competing Valence Bond Crystals in the Kagome Quantum Dimer Model
• Quantum dimer model for the spin-1/2 kagome Z2 spin liquid
• Impurity-doped Kagome Antiferromagnet: A Quantum Dimer Model Approach
• High temperature series expansion study of the Heisenberg antiferromagnet on the hyperkagome lattice: Comparison with Na${}_4$Ir${}_3$O${}_8$
• Phase diagram of an extended quantum dimer model on the hexagonal lattice
• Metamagnetic jump in the spin-1/2 antiferromagnetic Heisenberg model on the square-kagome lattice
• Microscopic theory of the nearest-neighbor valence bond sector of the spin-1/2 kagome antiferromagnet
• Double Semion Phase in an Exactly Solvable Quantum Dimer Model on the Kagome Lattice
• Frustrated topological symmetry breaking: geometrical frustration and anyon condensation
• Spin cluster operator theory for the Kagome lattice antiferromagnet
• Abundance of hard-hexagon crystals in the quantum pyrochlore antiferromagnet
• Staircase of crystal phases of hard-core bosons on the Kagome lattice
• ${\mathbb{Z}}_2$ gauge theory for valence bond solids on the kagome lattice
• Antiferromagnetism, $f$-wave and chiral $p$-wave superconductivity in a Kagome lattice with possible application to $s{d}^2$-graphenes
• How correlations change the magnetic structure factor of the kagome Hubbard model
• Linear independence of nearest-neighbor valence bond states in several two-dimensional lattices
• Spin-1/2 kagome Heisenberg antiferromagnet: Machine learning discovery of the spinon pair density wave ground state
• Statistical transmutation in doped quantum dimer models
• Statistics of holes and nature of superfluid phases in Quantum dimer models
• Field-induced superfluids and Bose liquids in Projected Entangled Pair States
• Optical conductivity of visons in Z2 spin liquids close to a VBS transition on the kagome lattice
• Emergent topological excitations in a two-dimensional quantum spin system
• Destroying a topological quantum bit by condensing Ising vortices
• Competing emergent Potts orders and possible nematic spin liquids in the Kagome $J_1-J_3$ Heisenberg model
• Engineering SU(2) invariant spin models to mimic quantum dimer physics on the square lattice
• Spin-phonon interactions on the kagome lattice: Dirac spin liquid versus valence-bond solids
• A continuous family of fully-frustrated Heisenberg model on the Kagome lattice
• Quantum-classical crossover in the spin-1/2 Heisenberg-Kitaev kagome magnet
• Chemistry of the spin-1/2 kagome Heisenberg antiferromagnet
• Dimer states of Rydberg atoms on the Kagome lattice as resources for universal measurement-based quantum computation
• Strong relevance of Zinc impurity in the spin-$\frac{1}{2}$ Kagome quantum antiferromagnets: a variational study