Some Details Concerning Transition from the Hubbard Model to the Heisenberg Model

In this paper we present the example the details of the transition of the Hubbard model to the Heisenberg model in the limit of on-site repulsion constant u → ∞. We explore the models with respect to the nearest and the next-nearest-neighbour hopping. We construct the next-nearest-neighbour hopping free subspaces for the considered example and find the procedure applicable to any number and any configuration of electrons in the chain. We found that some eigenvalues permute themselves for a specific value of the ratio of on-site repulsion constant to hopping constant and the effect is more visible the greater the next-nearest-neighbour hopping is. A similar situation occurs for eigenvectors. We also confirm SU(2)× SU(2) symmetry breaking when the next-nearest-neighbour hopping are considered.