Holes in the t-J(z) model: a diagrammatic study

The t-J(z) model is the strongly anisotropic limit of the t-J model which c aptures some general properties of doped antiferromagnets (AF's). The absen ce of spin fluctuations simplifies the analytical treatment of hole motion in an AF background, and allows us to calculate single- and two-hole spectr a with a high accuracy using a regular diagram technique combined with a re al-space approach. At the same time, numerical studies of this model via ex act diagonalization on small clusters show negligible finite-size effects f or a number of quantities, thus allowing a direct comparison between analyt ical and numerical results. Both approaches demonstrate that the holes have a tendency to pair in p- and d-wave channels at realistic values of t/J. I nteractions leading to pairing and effects selecting p and d waves are thor oughly investigated. The role of transverse spin fluctuations is considered using perturbation theory. Based on the results of the present study, we d iscuss the pairing problem in the realistic t-J-like model. Possible implic ations for preformed pairs formation and phase separation are drawn.