  We study the ground-state properties of trapped inhomogeneous systems of
hardcore bosons in two- and three-dimensional lattices. We obtain our results
both numerically, using quantum Monte Carlo techniques, and via several
analytical approximation schemes, such as the Gutzwiller-mean-field approach, a
cluster-mean-field method and a spin-wave analysis which takes quantum
fluctuations into account. We first study the homogeneous case, for which
simple analytical expressions are obtained for all observables of interest, and
compare the results with the numerical ones. We obtain the equation of state of
the system along with other thermodynamic properties such as the free energy,
kinetic energy, superfluid density, condensate fraction and compressibility. In
the presence of a trap, superfluid and insulating domains coexist in the
system. We show that the spin-wave-based method reproduces the quantum
Monte-Carlo results for global as well as for local quantities with a high
degree of accuracy. We also discuss the validity of the local density
approximation in those systems. Our analysis can be used to describe bosons in
optical lattices where the onsite interaction U is much larger than the hopping
amplitude t.
