Projected wave function study of Z2 spin liquids on the kagome lattice for spin-1/2 quantum Heisenberg antiferromagnet
Résumé
Motivated by recent density-matrix renormalization group (DMRG) calculations [S. Yan, D. A. Huse, and S. R. White, arXiv:1011.6114], 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 [Y.-M. Lu, Y. Ran, and P. A. Lee, arXiv:1104.1432], which gave a classification of all Schwinger-fermion mean-field fully symmetric Z2 spin liquids on the Kagome lattice, we thoroughly study 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 investigate 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 state-of-the-art optimization method, we are 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 towards the so-called Z2[0,\pi]\beta state, which was conjectured to describe the ground state obtained by the DMRG method.