Low-lying states of the extended Hubbard Model

Abstract

Allowing electrons to hop from one site to another with spin flipping enables one to modify the Hubbard model to include an additional term ν to adequately capture this action. The energy spectra of the first few states of this extended Hubbard model for different configurations up to eight-electron sites at half-filling is exactly obtained numerically for a one-dimensional ring. The results for the eight-site ring show that there are two distinct bands between the first few hundreds of energy eigenvalues separated by an energy gap; this gap is widest when ν is switched off but decreases rapidly as ν increases. This is an indication that at an appropriate value of ν, the band gap is likely to vanish thereby inducing a phase change. In addition, it is observed that there is always a phase change from antiferromagnetism to ferromagnetism when the nearest-neighbour Coulomb repulsion is an appropriate fraction of the on-site Coulomb energy.