Many-body basis-set reduction applied to the two-dimensional t-${\mathit{J}}_{\mathit{z}}$ model

A simple variation of the Lanczos method is discussed. The technique is based on a systematic reduction of the size of the Hilbert space of the model under consideration, and it has many similarities with the basis-set-reduction approach recently introduced by Wenzel and Wilson in the context of quantum chemistry. As an example, the two-dimensional t-${\mathit{J}}_{\mathit{z}}$ 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 ${\mathit{J}}_{\mathit{z}}$/t. In the bulk limit, the numerical results suggest that a finite coupling ${\mathit{J}}_{\mathit{z}}$/t${]}_{\mathit{c}}$∼0.18 is necessary to induce ‘‘binding’’ of holes in the model.