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Title: Many-body Green’s function theory for electron-phonon interactions: The Kadanoff-Baym approach to spectral properties of the Holstein dimer

We present a Kadanoff-Baym formalism to study time-dependent phenomena for systems of interacting electrons and phonons in the framework of many-body perturbation theory. The formalism takes correctly into account effects of the initial preparation of an equilibrium state and allows for an explicit time-dependence of both the electronic and phononic degrees of freedom. The method is applied to investigate the charge neutral and non-neutral excitation spectra of a homogeneous, two-site, two-electron Holstein model. This is an extension of a previous study of the ground state properties in the Hartree (H), partially self-consistent Born (Gd) and fully self-consistent Born (GD) approximations published in Säkkinen et al. [J. Chem. Phys. 143, 234101 (2015)]. Here, the homogeneous ground state solution is shown to become unstable for a sufficiently strong interaction while a symmetry-broken ground state solution is shown to be stable in the Hartree approximation. Signatures of this instability are observed for the partially self-consistent Born approximation but are not found for the fully self-consistent Born approximation. By understanding the stability properties, we are able to study the linear response regime by calculating the density-density response function by time-propagation. This amounts to a solution of the Bethe-Salpeter equation with a sophisticated kernel. Themore » results indicate that none of the approximations is able to describe the response function during or beyond the bipolaronic crossover for the parameters investigated. Overall, we provide an extensive discussion on when the approximations are valid and how they fail to describe the studied exact properties of the chosen model system.« less
Authors:
 [1] ;  [2] ;  [3] ;  [4] ;  [3] ;  [1]
  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. (Germany)
  4. Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin-Dahlem (Germany)
Publication Date:
OSTI Identifier:
22493337
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 143; Journal Issue: 23; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; BETHE-SALPETER EQUATION; BORN APPROXIMATION; DEGREES OF FREEDOM; DENSITY; DIMERS; ELECTRON-PHONON COUPLING; ELECTRONS; EQUILIBRIUM; EXCITATION; GREEN FUNCTION; GROUND STATES; HARTREE-FOCK METHOD; MANY-BODY PROBLEM; MATHEMATICAL SOLUTIONS; PERTURBATION THEORY; PHONONS; RESPONSE FUNCTIONS; SYMMETRY BREAKING; TIME DEPENDENCE