Many-body Green’s function theory for electron-phonon interactions: Ground state properties of the Holstein dimer

Journal Article · Mon Dec 21 00:00:00 EST 2015 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4936142· OSTI ID:22493336

Säkkinen, Niko; Leeuwen, Robert van ^[1]; Peng, Yang ^[2]; Appel, Heiko ^[3]

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1. Department of Physics, Nanoscience Center, University of Jyväskylä, Survontie 9, 40014 Jyväskylä (Finland)
2. Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin (Germany)
3. Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin-Dahlem (Germany)

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.

• OSTI ID: 22493336
• Journal Information: Journal of Chemical Physics, Vol. 143, Issue 23; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
37 INORGANIC
ORGANIC
PHYSICAL AND ANALYTICAL CHEMISTRY
BORN APPROXIMATION
COMPARATIVE EVALUATIONS
DIMERS
ELECTRON DENSITY
ELECTRON-PHONON COUPLING
ELECTRONS
GREEN FUNCTION
GROUND STATES
MANY-BODY PROBLEM
MATHEMATICAL SOLUTIONS
MOLECULES
OCCUPATION NUMBER
PERTURBATION THEORY
SYMMETRY BREAKING