Valence-bond crystals in the kagome spin-1/2 Heisenberg antiferromagnet: a symmetry classification and projected wave function study

Abstract

In this paper, we do a complete classification of valence-bond crystals (VBCs) on the kagome lattice based on general arguments of symmetry only and thus identify many new VBCs for different unit cell sizes. For the spin-1/2 Heisenberg antiferromagnet, we study the relative energetics of competing gapless spin liquids (SLs) and VBC phases within the class of Gutzwiller-projected fermionic wave functions using variational Monte Carlo techniques, hence implementing exactly the constraint of one fermion per site. By using a state-of-the-art optimization method, we conclusively show that the U(1) Dirac SL is remarkably stable towards dimerizing into all 6-, 12- and 36-site unit cell VBCs. This stability is also preserved on addition of a next-nearest-neighbor super-exchange coupling of both antiferromagnetic and ferromagnetic (FM) type. However, we find that a 36-site unit cell VBC is stabilized on addition of a very small next-nearest-neighbor FM super-exchange coupling, i.e. |J2|~0.045, and this VBC is the same in terms of space-group symmetry as that obtained in an effective quantum dimer model study. It breaks reflection symmetry, has a nontrivial flux pattern and is a strong dimerization of the uniform RVB SL.

arXiv comment16 pages, 25 figures. Invited paper for Focus issue on "Quantum Spin Liquids" of the New Journal of Physics

References in corpus (50)

• Spin Liquid Ground State of the $S=1/2$ Kagome Heisenberg Model
• Quantum Orders and Symmetric Spin Liquids
• Spin Dynamics of the Spin-1/2 Kagome Lattice Antiferromagnet ZnCu_3(OH)_6Cl_2
• Projected wavefunction study of Spin-1/2 Heisenberg model on the Kagome lattice
• Quantum magnetism in the paratacamite family: towards an ideal kagome lattice
• First excitations of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice
• Generalized Lanczos Algorithm for Variational Quantum Monte Carlo
• Order versus Disorder in the Quantum Heisenberg Antiferromagnet on the Kagom{é} lattice: an approach through exact spectra analysis
• 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
• Wave function optimization in the variational Monte Carlo method
• Spin Liquid States on the Triangular and Kagome Lattices: A Projective Symmetry Group Analysis of Schwinger Boson States
• Ground State of the Kagome Lattice Heisenberg Antiferromagnet
• Dirac, Anderson, and Goldstone on the Kagome
• Two spin liquid phases in the spatially anisotropic triangular Heisenberg model
• Frustrated antiferromagnets with entanglement renormalization: ground state of the spin-1/2 Heisenberg model on a kagome lattice
• Quantum spin liquid states in the two dimensional kagome antiferromagnets, ZnxCu4-x(OD)6Cl2
• Quantum Kagome antiferromagnet ZnCu3(OH)6Cl2
• The kagome antiferromagnet: a chiral topological spin liquid ?
• The magnetic groundstate of an experimental $S=1/2$ kagomé antiferromagnet
• Projected wave function study of Z2 spin liquids on the kagome lattice for the spin-1/2 quantum Heisenberg antiferromagnet
• Spin-1/2 Heisenberg-Antiferromagnet on the Kagome Lattice: High Temperature Expansion and Exact Diagonalisation Studies
• Physics of low energy singlet states of the Kagome lattice quantum Heisenberg antiferromagnet
• Z2 spin liquid in S=1/2 Heisenberg model on Kagome lattice: A projective symmetry group study of Schwinger-fermion mean-field states
• Magneto-thermodynamics of the spin-1/2 Kagome antiferromagnet
• ^{63}Cu, ^{35}Cl, and ^{1}H NMR in the S=1/2 Kagomé Lattice ZnCu_{3}(OH)_{6}Cl_{2}
• Topological and Entanglement Properties of Resonating Valence Bond wavefunctions
• Numerical-Diagonalization Study of Spin Gap Issue of the Kagome Lattice Heisenberg Antiferromagnet
• Ground-State Energy and Spin Gap of Spin-1/2 Kagome Heisenberg Antiferromagnetic Clusters: Large Scale Exact Diagonalization Results
• Quantum magnetism in two dimensions: From semi-classical Néel order to magnetic disorder
• Low temperature magnetization of the S=1/2 kagome antiferromagnet ZnCu_3(OH)_6Cl_2
• Interplay of thermal and quantum spin fluctuations on the kagome lattice
• Low energy excitations of the kagome antiferromagnet and the spin gap issue
• Triplet and Singlet Excitations in the Valence Bond Crystal Phase of Kagome Lattice Heisenberg Model
• Fingerprints of spin-orbital entanglement in transition metal oxides
• Synthesis and Characterization of Single Crystal Samples of Spin-$1/2$ Kagome Lattice Antiferromagnets in the Zn-Paratacamite Family Zn${}_x$Cu${}_{4-x}$(OH)${}_6$Cl${}_2$
• 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
• Effective Quantum Dimer Model for the Kagome Heisenberg Antiferromagnet: Nearby Quantum Critical Point and Hidden Degeneracy
• Spin Liquid Ground State in the Frustrated Kagome Antiferromagnet MgCu3(OH)6Cl2
• Hidden long range order in Heisenberg Kagome antiferromagnets
• Variational study of J1-J2 Heisenberg model on Kagome lattice using projected Schwinger boson wave functions
• Generalized Hardcore Dimer Models approach to low-energy Heisenberg frustrated antiferromagnets: general properties and application to the kagome antiferromagnet
• Weak Ferromagnetic Exchange and Anomalous Specific Heat in ZnCu3(OH)6Cl2
• Competing Valence Bond Crystals in the Kagome Quantum Dimer Model
• Impurity-doped Kagome Antiferromagnet: A Quantum Dimer Model Approach
• Sign structures for short-range RVB states on small kagome clusters
• Neel and Valence Bond Crystal Order on a Distorted Kagome Lattice: Implications For Zn-Paratacamite
• Low-energy singlet dynamics of spin-$\frac{1}{2}$ kagome Heisenberg antiferromagnets
• Frustrated RVB states in 2D: classifications and short-range correlations

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• First-principles determination of Heisenberg Hamiltonian parameters for the spin-1/2 kagome antiferromagnet ZnCu3(OH)6Cl2
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• Spin-1/2 kagome Heisenberg antiferromagnet: Machine learning discovery of the spinon pair density wave ground state
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• A primer on Kitaev Model: Basic aspects, material realization, and recent experiments
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