title: Many-body Green's function theory for electron-phonon interactions: Ground state properties of the Holstein dimer.
abstract: We study ground-state properties of a two-site, two-electron Holstein model describing two molecules coupled indirectly via electron-phonon interaction by using both exact diagonalization and self-consistent diagrammatic many-body perturbation theory. The Hartree and self-consistent Born approximations used in the present work are studied at different levels of self-consistency. The governing equations are shown to exhibit multiple solutions when the electron-phonon interaction is sufficiently strong, whereas at smaller interactions, only a single solution is found. The additional solutions at larger electron-phonon couplings correspond to symmetry-broken states with inhomogeneous electron densities. A comparison to exact results indicates that this symmetry breaking is strongly correlated with the formation of a bipolaron state in which the two electrons prefer to reside on the same molecule. The results further show that the Hartree and partially self-consistent Born solutions obtained by enforcing symmetry do not compare well with exact energetics, while the fully self-consistent Born approximation improves the qualitative and quantitative agreement with exact results in the same symmetric case. This together with a presented natural occupation number analysis supports the conclusion that the fully self-consistent approximation describes partially the bipolaron crossover. These results contribute to better understanding how these approximations cope with the strong localizing effect of the electron-phonon interaction.
authors.affiliation: Department of Physics, Nanoscience Center, University of Jyväskylä, Survontie 9, 40014 Jyväskylä, Finland.
authors.forename: Niko
authors.initials: N
authors.lastname: Säkkinen
authors.affiliation: Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany.
authors.forename: Yang
authors.initials: Y
authors.lastname: Peng
authors.affiliation: Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin-Dahlem, Germany.
authors.forename: Heiko
authors.initials: H
authors.lastname: Appel
authors.affiliation: Department of Physics, Nanoscience Center, University of Jyväskylä, Survontie 9, 40014 Jyväskylä, Finland.
authors.forename: Robert
authors.initials: R
authors.lastname: van Leeuwen