  Using quantum Monte Carlo (QMC) simulations and a mean field (MF) theory, we
investigate the spin-1/2 XXZ model with nearest neighbor interactions on a
periodic depleted square lattice. In particular, we present results for 1/4
depleted lattice in an applied magnetic field and investigate the effect of
depletion on the ground state. The ground state phase diagram is found to
include an antiferromagnetic (AF) phase of magnetization $m_{z}=\pm 1/6$ and an
in-plane ferromagnetic (FM) phase with finite spin stiffness. The agreement
between the QMC simulations and the mean field theory based on resonating
trimers suggests the AF phase and in-plane FM phase can be interpreted as a
Mott insulator and superfluid of trimer states respectively. While the thermal
transitions of the in-plane FM phase are well described by the
Kosterlitz-Thouless transition, the quantum phase transition from the AF phase
to in-plane FM phase undergo a direct second order insulator-superfluid
transition upon increasing magnetic field.
