By using the variational Monte Carlo technique, we study the spin-$\frac{1}{2}$ XXZ antiferromagnetic model (with easy-plane anisotropy) on the kagome lattice. A class of Gutzwiller projected fermionic states with a spin Jastrow factor is considered to describe either spin liquids [with $U\left(1\right)$ or $Z_2$ symmetry] or magnetically ordered phases [with $\mathbf{q}=(0,0)$ or $\mathbf{q}=(4\pi /3,0)$]. We find that the magnetic states are not stable in the thermodynamic limit. Moreover, there is no energy gain to break the gauge symmetry from $U\left(1\right)$ to $Z_2$ within the spin-liquid states, as previously found in the Heisenberg model. The best variational wave function is therefore the $U\left(1\right)$ Dirac state, supplemented by the spin Jastrow factor. Furthermore, a vanishing $S=2$ spin gap is obtained at the variational level, in the whole regime from the $XY$ to the Heisenberg model.

• Received 31 May 2015

DOI:https://doi.org/10.1103/PhysRevB.92.201105