Two-particle correlations in the one-dimensional Hubbard model: a ground-state analytical solution

Abstract

A solution to the extended Hubbard Hamiltonian for the case of two-particles in an infinite one-dimensional lattice is presented, using a real-space mapping method and the Green function technique. This Hamiltonian considers the on-site ($U$) and the nearest-neighbor ($V$) interactions. The method is based on mapping the correlated many-body problem onto an equivalent site-impurity tight-binding one in a higher dimensional space. In this new space we obtained the analytical solution for the ground state binding energy. Results are in agreement with the numerical solution obtained previously \cite{nw92}, and with those obtained in the reciprocal space \cite% {mh90}.