The effective single-band Hamiltonian for holes in the two-dimensional quantum antiferromagnet, relevant for the ${\mathrm{CuO}}_2$ layers in copper-oxide superconductors, is studied by the exact diagonalization of a finite-size system with 16 cells. Single- and two-hole ground-state properties are calculated. Pair-binding-energy and hole-density correlation functions indicate that two holes bind for moderate exchange interactions, even in the case of the extreme anisotropic-Ising limit.

• Received 18 October 1988

DOI:https://doi.org/10.1103/PhysRevB.39.7074