Projected wave function study of Z2 spin liquids on the kagome lattice for the spin-1/2 quantum Heisenberg antiferromagnet

Abstract

Motivated by recent density-matrix renormalization group (DMRG) calculations [Yan, Huse, and White, Science 332, 1173 (2011)], which claimed that the ground state of the nearest-neighbor spin-1/2 Heisenberg antiferromagnet on the kagome lattice geometry is a fully gapped spin liquid with numerical signatures of Z2 gauge structure, and a further theoretical work [Lu, Ran, and Lee, Phys. Rev. B 83, 224413 (2011)], which gave a classification of all Schwinger-fermion mean-field fully symmetric Z2 spin liquids on the kagome lattice, we have thoroughly studied Gutzwiller-projected fermionic wave functions by using quantum variational Monte Carlo techniques, hence implementing exactly the constraint of one fermion per site. In particular, we investigated the energetics of all Z2 candidates (gapped and gapless) that lie in the neighborhood of the energetically competitive U(1) gapless spin liquids. By using a state-of-the-art optimization method, we were able to conclusively show that the U(1) Dirac state is remarkably stable with respect to all Z2 spin liquids in its neighborhood, and in particular for opening a gap toward the so-called Z2[0,π]β state, which was conjectured to describe the ground state obtained by the DMRG method. Finally, we also considered the addition of a small second nearest-neighbor exchange coupling of both antiferromagnetic and ferromagnetic type, and obtained similar results, namely, a U(1) Dirac spin-liquid ground state.

5 pages + supplementary material (2 pages), 3 figures, 1 Table: Final published version, selected as an Editor's suggestion

References in corpus (12)

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• Low temperature magnetization of the S=1/2 kagome antiferromagnet ZnCu_3(OH)_6Cl_2
• Valence-bond crystal in the extended kagome spin-1/2 quantum Heisenberg antiferromagnet: A variational Monte Carlo approach
• 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

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• Phase diagram of the J1-J2 Heisenberg model on the kagome lattice
• Haydeeite: a spin-1/2 kagome ferromagnet
• Chern-Simons theory of the magnetization plateaus of the spin-1/2 quantum XXZ Heisenberg model on Kagome Lattice
• Detecting crystal symmetry fractionalization from the ground state: Application to ${\mathbb{Z}}_2$ spin liquids on the kagome lattice
• Valence-bond crystals in the kagome spin-1/2 Heisenberg antiferromagnet: a symmetry classification and projected wave function study
• Spin-1/2 Heisenberg antiferromagnet on an anisotropic kagome lattice
• Influence of Dzyaloshinskii-Moriya interactions on magnetic structure of a spin-1/2 deformed kagome lattice antiferromagnet
• Tuning of magnetic frustration in $S=1/2$ Kagomé lattices {[Cu${}_3$(CO${}_3$)${}_2$$(bpe{)}_3$](ClO${}_4$)${}_2$}${}_n$ and {[Cu${}_3$(CO${}_3$)${}_2$$(bpy{)}_3$](ClO${}_4$)${}_2$}${}_n$ through rigid and flexible ligands