On the Internal Structure of the Singlet d$_{X^2-Y^2}$ Hole Pair in an Antiferromagnet

Abstract

Exact diagonalizations of two dimensional small t--J clusters reveal dominant hole-hole correlations at distance $\sqrt{2}$ (ie between holes on next nearest neighbor sites). A new form of singlet $d_{x^2-y^2}$ pair operator is proposed to account for the spatial extention of the two hole-bound pair beyond nearest neighbor sites.