Basis Set Reduction Applied to the Two Dimensional t-Jz Model

A simple variation of the Lanczos method is discussed. The new technique is based on a systematic reduction of the size of the Hilbert space of the model under consideration. As an example, the two dimensional ${\rm t-J_z}$ model of strongly correlated electrons is studied. Accurate results for the ground state energy can be obtained on clusters of up to 50 sites, which are unreachable by conventional Lanczos approaches. In particular, the energy of one and two holes is analyzed as a function of ${\rm J_z/t}$. In the bulk limit, it is shown that a finite coupling ${\rm J_z/t ]_c} \sim 0.18$ is necessary to induce ``binding'' of holes in the model. It is argued that this result implies that the two dimensional ${\rm t-J}$ model phase separates only for couplings larger than a $finite$ critical value.