Two-site two-electron generalized Hubbard–Holstein model: a perturbation study

The two-site two-electron generalized Hubbard–Holstein model is studied within a perturbation method based on a variational phonon basis obtained through the modified Lang–Firsov (MLF) transformation. The ground-state wave function and the energy are found including up to the seventh and eighth order of perturbation, respectively. The convergence of the perturbation corrections to the ground state energy, as well as to the correlation functions, are investigated. The kinetic energy and the correlation functions involving charge and lattice deformations are studied as a function of electron–phonon(e–ph) coupling and electron–electron interactions for different values of the adiabaticity parameter. The simultaneous effect of the e–ph coupling and Coulomb repulsion on the kinetic energy shows interesting features.