Holes in the t-J_z model: a thorough study

TL;DR

This paper provides a comprehensive analytical and numerical study of the t-J_z model, revealing hole pairing tendencies and the effects of spin fluctuations, with implications for understanding pairing in doped antiferromagnets.

Contribution

It offers a detailed comparison of analytical and numerical results for the t-J_z model, highlighting hole pairing mechanisms and the influence of spin fluctuations.

Findings

Holes tend to pair in p- and d-wave channels at realistic t/J values.

Analytical and numerical methods show negligible finite size effects.

Transverse spin fluctuations influence pairing interactions.

Abstract

The t-J_z model is the strongly anisotropic limit of the t-J model which captures some general properties of the doped antiferromagnets (AF). The absence of spin fluctuations simplifies the analytical treatment of hole motion in an AF background and allows us to calculate the single- and two-hole spectra with high accuracy using regular diagram technique combined with real-space approach. At the same time, numerical studies of this model via exact diagonalization (ED) on small clusters show negligible finite size effects for a number of quantities, thus allowing a direct comparison between analytical and numerical results. Both approaches demonstrate that the holes have tendency to pair in the p- and d-wave channels at realistic values of t/J. The interactions leading to pairing and effects selecting p and d waves are thoroughly investigated. The role of transverse spin fluctuations is considered using perturbation theory. Based on the results of the present study, we discuss the pairing problem in the realistic t-J-like model. Possible implications for preformed pairs formation and phase separation are drawn.