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/t${\mathrm{\Vert }}_{\mathit{c}}$ The symmetry of the bound state is ${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$. We also observed that its ‘‘quasiparticle’’ weight ${\mathit{Z}}_{2\mathit{h}}$ (defined in the text), is finite for coupling J/t≥J/t${\mathrm{\Vert }}_{\mathit{c}}$. Thus, in the region J/t≥J/t${\mathrm{\Vert }}_{\mathit{c}}$ the bound state of two holes behaves like a quasiparticle with charge Q=2e, spin S=0, and ${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$ internal symmetry. The relation with recent ideas that have suggested the possibility of d-wave pairing in theories of the high-${\mathit{T}}_{\mathit{c}}$ cuprates is briefly discussed.