Yasir Iqbal, Federico Becca, Didier Poilblanc
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 liquid 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 spin liquid 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 type. However, we find that a 36-site unit cell VBC is stabilized on addition of a very small next-nearest-neighbor ferromagnetic super-exchange coupling, i.e., $|J_{2}|\approx0.045$ and this VBC is the same in terms of space-group symmetry as the one obtained in an effective quantum dimer model study. It breaks reflection symmetry, has a non-trivial flux pattern and is a strong dimerization of the uniform RVB spin liquid.
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http://arxiv.org/abs/1203.3421
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