Phase separation in mixtures of hard core bosons

A theoretical investigation of boson versions of the t-J and t-J(z) models on the square lattice is carried out. In the t-J(z) model, phase separation between a hole-rich and a hole-free phase occurs, at sufficiently low hole doping, for arbitrarily small values of J(z). The boson t-J model, instead, features a uniform ground state at any doping for J/t less than or equal to 1.5. No evidence of a striped ground state is found. Relevance of this study to the corresponding fermion models is discussed. Fermi statistics is found to enhance the tendency toward phase separation: in particular, phase separation is predicted, at low doping, in the fermion t-J(z) model, at all values of J(z).