The Hamiltonian for an extended Hubbard model with phonons as introduced by A. Montorsi and M. Rasetti is considered on a D-dimensional lattice. The symmetries of the model are studied in various cases. It is shown that for a certain choice of the paramet
The one-dimensional Hubbard model is known to possess an extended su(2) symmetry and to be integrable. I indroduce an integrable model with an extended su(n) symmetry. This model contains the usual su(2) Hubbard model and has a set of features that make it the su(n) generalization of the Hubbard model. Complete integrability is shown by introducing the L-matrix and showing that the transfer matrix commutes with the hamiltonian. While the model is integrable in one dimension, it provides a generalization of the Hubbard hamiltonian in any dimension.
The phase diagrams and electron orderings of the half-filled extended Hubbard models with anisotropic spin-exchange interactions (J⊥, J||) are studied. The cases of ferromagnetic (Jα 0) exchange couplings are considered for repulsive on-site interaction (U ≥ 0). The analysis of these t–U–J||–J⊥ models is performed for d-dimensional hypercubic lattices including d = 1 and d = ∞ by means of the (broken symmetry) HFA supplemented, for d = ∞, by the slave-boson mean-field method. The basic features of the derived phase diagrams are discussed.