The generalized Hubbard model: a solution for the binding of three particles in a linear chain

The binding problem is studied within the generalized Hubbard Hamiltonian b y using a real-space method. This method is an extension of the previously proposed mapping method for the simple Hubbard model in order to include th e bond-charge interaction term. The generalization of the method is based o n mapping the correlated many-body problem onto an equivalent site- and bon d-impurity tight-binding one in a higher dimensional space, where the probl em can be solved exactly. The three particles correlation in a linear chain has been analyzed by calculating the binding energy using different values of the bond-charge, the on-site (U) and the nearest-neighbor (V) interacti ons. A bound state asymmetry between electrons and holes was found for bond -charge interactions. Also, an analytical solution is obtained for some spe cial values of the hopping parameters and for all kind of interactions in t he Hubbard Hamiltonian. (C) 2001 Elsevier Science B.V. All rights reserved.