  Employing large-scale quantum Monte Carlo simulations, we study the extended
$XXZ$ model on the kagome lattice. A $\mathbb Z_2$ quantum spin liquid phase
with effective even Ising gauge field structure emerges from the delicate
balance among three symmetry-breaking phases including stripe solid, staggered
solid and ferromagnet. This $\mathbb{Z}_2$ spin liquid is stabilized by an
extended interaction related to the Rokhsar-Kivelson potential in the quantum
dimer model limit. The phase transitions from the staggered solid to a spin
liquid or ferromagnet are found to be first order and so is the transition
between the stripe solid and ferromagnet. However, the transition between a
spin liquid and ferromagnet is found to be continuous and belongs to the 3D
$XY^*$ universality class associated with the condensation of spinons. The
transition between a spin liquid and stripe solid appears to be continuous and
associated with the condensation of visons.

Strongly Correlated Electrons