  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,{\pi}]{\beta} 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.
