Eur. Phys. J. B 18, 9-16 (2000)
https://doi.org/10.1007/s100510070071

Non perturbative calculations for three particles in a linear chain within the generalized Hubbard model

¹ Instituto de Investigaciones en Materiales, UNAM, Apartado Postal 70-360, 04510 México DF, México
² Facultad de Ciencias Físico-Matemáticas (Posgrado en Optoelectrónica) BUAP, Puebla Pue., México
³ Instituto de Física BUAP, Puebla Pue., México
⁴ Laboratoire d'Études des Propriétés Électroniques des Solides, CNRS, BP 166, 38042 Grenoble Cedex 9, France

Received: 21 January 2000
Revised: 18 July 2000
Published online: 15 November 2000

Abstract

A real-space method has been introduced to study the pairing problem within the generalized Hubbard Hamiltonian. This method includes the bond-charge interaction term as an extension of the previously proposed mapping method [1] for the Hubbard model. The generalization of the method is based on mapping the correlated many-body problem onto an equivalent site- and bond-impurity tight-binding one in a higher dimensional space, where the problem can be solved exactly. In a one-dimensional lattice, we analyzed the three particle correlation by calculating the binding energy at the ground state, using different values of the bond-charge, the on-site (U) and the nearest-neighbor (V) interactions. A pairing asymmetry is found between electrons and holes for the generalized hopping amplitude, where the hole pairing is not always easier than the electron case. For some special values of the hopping parameters and for all kinds of interactions in the Hubbard Hamiltonian, an analytical solution is obtained.