Real-space configurations of two holes in a quantum antiferromagnet

The coupled Eliashberg-like integral equations for the self-energy and the pairing amplitude of two holes in real space are derived within the t-J model. From the calculation of the Eliashberg spectral density function α2F(ω), the configurations of two holes in real space can be determined. It is found that two holes on adjacent sites have the strongest attractive interaction, but the pairing amplitude vanishes. This indicates that the holes cannot form local pairs within the t-J model regardless of whether the effective interaction between the holes is attractive. The spectral function of the holes is calculated. At the strong-coupling limit, the similarity between our result for a single hole and that of the retraceable-path approximation of Brinkman and Rice is also discussed