  We investigate the properties in finite magnetic field of an extended
anisotropic XXZ spin-1/2 model on the Kagome lattice, originally introduced by
Balents, Fisher, and Girvin [Phys. Rev. B, 65, 224412 (2002)]. The
magnetization curve displays plateaus at magnetization m=1/6 and 1/3 when the
anisotropy is large. Using low-energy effective constrained models (quantum
loop and quantum dimer models), we discuss the nature of the plateau phases,
found to be crystals that break discrete rotation and/or translation
symmetries. Large-scale quantum Monte-Carlo simulations were carried out in
particular for the m=1/6 plateau. We first map out the phase diagram of the
effective quantum loop model with an additional loop-loop interaction to find
stripe order around the point relevant for the original model as well as a
topological Z2 spin liquid. The existence of a stripe crystalline phase is
further evidenced by measuring both standard structure factor and entanglement
entropy of the original microscopic model.
