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.

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

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• Pinch-points to half-moons and up in the stars: the kagome skymap
• Gutzwiller-projected states for the $J_1$-$J_2$ Heisenberg model on the kagome lattice: achievements and pitfalls
• Valence bond phases of herbertsmithite and related copper kagome materials
• Spin-1/2 kagome Heisenberg antiferromagnet: Machine learning discovery of the spinon pair density wave ground state
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• Spin-phonon interactions on the kagome lattice: Dirac spin liquid versus valence-bond solids
• Projective symmetry group classification of Abrikosov fermion mean-field ansätze on the square-octagon lattice
• Thermal features of Heisenberg antiferromagnets on edge- versus corner-sharing triangular-based lattices: A message from spin waves
• Strong relevance of Zinc impurity in the spin-$\frac{1}{2}$ Kagome quantum antiferromagnets: a variational study
• A primer on Kitaev Model: Basic aspects, material realization, and recent experiments
• Semi-Dirac spin liquids and frustrated quantum magnetism on the trellis lattice
• Quantum phase diagram of the spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the square-kagome lattice: a tensor network study