  Motivated by recent experiments on two-component systems, we investigate the
ground-state phase diagram of a mixture of two bosonic species by means of
path-integral quantum Monte Carlo by the two-worm algorithm. The mixture is
trapped in a square lattice at half-filling conditions. Various quantum phases
are stabilized depending on the interplay between intra- and inter-species
interactions. We show that the phase diagram features a demixed superfluid
phase and demixed Mott-Insulator phase when the inter-species interaction
becomes greater than the intra-species repulsion, and a double-superfluid phase
or a supercounterflow otherwise. We also show that demixing, characterized by
spatial separation of the two species, can be detected experimentally through
the effects of anisotropy revealed by time-of-flight images.
