d-wave bound state of holes in an antiferromagnet

The formation of bound states of holes in an antiferromagnetic spin-1/2 background is studied using numerical techniques applied to the t-J Hamiltonian on clusters with up to 26 sites. An analysis of the binding energy as a function of cluster size suggests that a two-hole bound state is formed for couplings larger than a ``critical'' value J/tc The symmetry of the bound state is dₓ²-y². We also observed that its ``quasiparticle'' weight Z₂ₕ (defined in the text), is finite for coupling J/t{≥}J/tc. Thus, in the region J/t{≥}J/tc the bound state of two holes behaves like a quasiparticle with charge Q=2e, spin S=0, and dₓ²-y² internal symmetry. The relation with recent ideas that have suggested the possibility of d-wave pairing in theories of the high-Tc cuprates is briefly discussed.