Hole pairing and flux quantization in model Cu-O clusters

In the three-band Hubbard model, the fully symmetric Cu-O clusters with a central Cu and appropriate hole numbers have many-body ground states in which holes are paired. Here we investigate the mechanism of pairing, focusing on clusters with less than or equal to 21 atoms and 4 holes. We show that spin-flip diagrams yield the effective interaction. The analysis agrees with the results of exact diagonalization and shows that singlet-triplet splitting measures the strength of the pairing interaction. Moreover the quantization at half-integer values of a magnetic text flux is consistent with superconducting pairing.