Formation of clusters in the two dimensional t-J model: The mechanism for phase separation

The emergence of phase separation is investigated in the framework of a 2D t-J model by means of a variational product ansatz, which covers the infinite lattice by two types of L x L clusters. Clusters of the first type are completely occupied with electrons, i.e. they carry maximal charge Q_e=L^2 and total spin 0, and thereby form the antiferromagnetic background. Holes occur in the second type of clusters -- called ``hole clusters''. They carry a charge Q_h<L^2. The charge Q_h and the number N(Q_h) of hole clusters is fixed by minimizing the total energy at given hole density and spin exchange coupling \alpha=J/t. For \alpha not too small (\alpha>0.5) it turns out that hole clusters are occupied with an even number Q_h<L^2 of electrons and carry a total spin 0. For increasing \alpha the charge Q_h(\alpha) of the hole clusters decreases.Some points on the boundary curve can be extracted from Q_h(\alpha).