Exact solutions for a single hole in a 'high-Tc' model

Abstract

The author solves the d-p model for one very particular band filling in two very particular limits: one hole per copper site and one extra hole on an oxygen site. He analyses the case when the hybridisation energy is the smallest and the repulsion between holes on copper sites is the largest energy in the problem. The two limits considered are when the oxygen band is, firstly, near the lower copper Hubbard band and, secondly, near the upper copper Hubbard band, as the copper Hubbard constant diverges. As the hybridisation vanishes, the spin system on the copper sites becomes degenerate and he asks how the inclusion of the extra hole breaks that degeneracy, assuming that the antiferromagnetic superexchange is dominated by the motion of the hole. In the limit where the oxygen band is near the lower copper Hubbard band, Nagaoka ferromagnetism in two dimensions is found for the 'normal' case, with the hole spin parallel to the copper spin system. In the limit where the oxygen band is near the upper copper Hubbard band, Nagaoka ferromagnetism in two dimensions is found with the hole binding a spin antiparallel to the copper spin system in its own near vicinity. For the planar arrangement of CuO2, it is found that the oxygen lattice coupled by the copper lattice is not 'normal' and is strongly frustrated.