Electronic and phononic states of the Holstein-Hubbard dimer of variable length: A variational approach

A polaronic Hamiltonian is obtained for a dimer of length a, including an E instein phonon of frequency Omega, a Holstein coupling g(0), and all the el ectronic one- and two-body terms consistent with a single orbital per site (the latter evaluated in terms of Wannier functions built from Gaussian ato mic orbitals). In the quarter- and half-filled orbital cases, the possible ground states for varying a, at given g(0) and Omega, are identified by ind ependent and simultaneous optimization of the electronic and phononic param eters.