We solve exactly a ${\mathrm{Cu}}_4$${\mathrm{O}}_8$ cluster with four and five holes, for parameters for which the low-energy physics of the three-band Hubbard model can be mapped exactly to a t-J model with J=0. When a Cu-Cu superexchange J is included, the mapping is no more exact. We investigate the quality of the mapping and the amount of nonorthogonal Zhang-Rice singlets of each low-energy eigenstate as a function of J. We also explain briefly how to calculate a property of the three-band model (such as the Cu and O photoemission intensity) using the t-J model.

• Received 10 December 1993

DOI:https://doi.org/10.1103/PhysRevB.49.16048