Generalized Hardcore Dimer Models approach to low-energy Heisenberg frustrated antiferromagnets: general properties and application to the kagome antiferromagnet

Abstract

We propose a general non-perturbative scheme that quantitatively maps the low-energy sector of spin-1/2 frustrated Heisenberg antiferromagnets to effective Generalized Quantum Dimer Models. We develop the formal lattice independent frame and establish some important results on (i) the locality of the generated Hamiltonians (ii) how full resummations can be performed in this renormalization scheme. The method is then applied to the much debated kagome antiferromagnet for which a fully resummed effective Hamiltonian - shown to capture the essential properties and provide deep insights on the microscopic model [D. Poilblanc, M. Mambrini and D. Schwandt, arXiv:0912.0724] - is derived.

26 pages, 4 figures, EPAPS inlined, manuscript revised, corrected minor typos (notably figure 2).

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• Plaquette valence bond solid in the frustrated Heisenberg quantum antiferromagnet on the square lattice
• Physics of low energy singlet states of the Kagome lattice quantum Heisenberg antiferromagnet
• Magneto-thermodynamics of the spin-1/2 Kagome antiferromagnet
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• Global phase diagrams of frustrated quantum antiferromagnets in two dimensions: doubled Chern-Simons theory
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• Doping quantum dimer models on the square lattice
• Valence Bond Solid Phases on Deformed Kagome Lattices: Application to Rb2Cu3SnF12
• Properties of holons in the Quantum Dimer Model
• Magnetic field-induced transition in a quantum magnet described by the Quantum Dimer Model

Cited by in corpus (38)

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• Prediction of Toric Code Topological Order from Rydberg Blockade
• Phase Diagram of a Frustrated Quantum Antiferromagnet on the Honeycomb Lattice: Magnetic Order versus Valence-Bond Crystal formation
• Projected wave function study of Z2 spin liquids on the kagome lattice for the spin-1/2 quantum Heisenberg antiferromagnet
• Vanishing spin gap in a competing spin-liquid phase in the kagome Heisenberg antiferromagnet
• The $S=1/2$ Kagome Heisenberg Antiferromagnet Revisited
• Nature of chiral spin liquids on the kagome lattice
• 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
• Properties of Resonating-Valence-Bond Spin Liquids and Critical Dimer Models
• Extended quantum U(1)-liquid phase in a three-dimensional quantum dimer model
• Frustrated magnetism and resonating valence bond physics in two-dimensional kagome-like magnets
• Transition to a many-body localized regime in a two-dimensional disordered quantum dimer model
• Quantum spin liquid in the semiclassical regime
• Valence-bond crystals in the kagome spin-1/2 Heisenberg antiferromagnet: a symmetry classification and projected wave function study
• Spin Hamiltonians with resonating-valence-bond ground states
• Resonating valence bond wavefunctions and classical interacting dimer models
• 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
• Competing Valence Bond Crystals in the Kagome Quantum Dimer Model
• Resonating valence bond physics is not always governed by the shortest tunneling loops
• Quantum dimer model for the spin-1/2 kagome Z2 spin liquid
• Impurity-doped Kagome Antiferromagnet: A Quantum Dimer Model Approach
• Microscopic theory of the nearest-neighbor valence bond sector of the spin-1/2 kagome antiferromagnet
• Spin-1/2 Heisenberg antiferromanget on kagome: a $Z_2$ spin liquid with fermionic spinons
• ${\mathbb{Z}}_2$ gauge theory for valence bond solids on the kagome lattice
• 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
• Statistics of holes and nature of superfluid phases in Quantum dimer models
• Dimer description of the SU(4) antiferromagnet on the triangular lattice
• Anyon condensation and confinement transition in a Kitaev spin liquid bilayer
• Engineering SU(2) invariant spin models to mimic quantum dimer physics on the square lattice
• Ising nematic fluid phase of hard-core dimers on the square lattice
• Classical fully-packed loop model with attractive interactions on the square lattice
• Extended Quantum Dimer Model and novel valence-bond phases
• Continuous interpolation between the fully frustrated Ising and quantum dimer models
• Vison condensation and spinon confinement in a kagome-lattice ${\mathbb{Z}}_2$ spin liquid: A numerical study of a quantum dimer model
• Entanglement studies of resonating valence bonds on the frustrated square lattice