Hole pairing and clustering in the two-dimensionalt-Jmodel

Hole-density correlation functions in the t-J model on lattices with square geometry are studied by the method of exact diagonalization for systems of various sizes with up to 26 sites. For the largest sizes we employ only a restricted basis, whereby for the extrapolation we introduce and test a scaling procedure. For two holes in an antiferromagnet our results confirm their binding for J>${\mathit{J}}_{\mathit{c}}$∼0.2t. For four holes the two-point and four-point density correlations, calculated for N=18,20 sites, show clear evidence for hole-clustering instabilities for J>${\mathit{J}}_{\mathit{s}}$∼1.5t; a first instability is likely to be towards a striped phase, with holes forming domain walls along the (0,1) or (1,0) direction. Signs for the phase separation into a hole-rich and a hole-free phase appear only at J>${\mathit{J}}_{\mathit{s}}^{\mathrm{*}}$∼2.5t. Results in the intermediate regime 0.4<J/t<1.2 are consistent with the pairing picture, although there are also indications for a large weight of configurations representing domain walls along the (1,1) direction.