Numerical study of the spin-flop transition in anisotropic spin-$\frac{1}{2}$ antiferromagnets

Magnetization processes of the spin-1/2 antiferromagnetic $\mathrm{XXZ}$ model in two and three spatial dimensions are studied using a quantum Monte Carlo method based on stochastic series expansions. A recently developed operator-loop algorithm enables us to show clear evidence of a first-order phase transition in the presence of an external magnetic field. Phase diagrams of closely related systems, hard core bosons with nearest-neighbor repulsions, are also discussed, focusing on the possibilities of phase-separated and supersolid phases.