Barišić, Osor S. and Barišić, Slaven (2005) Polarons by translationally invariant diagrammatic perturbation theory. Fizika A, 14 (2). pp. 153166. ISSN 13300008

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Abstract
The structure of the translationallyinvariant diagrammatic perturbation theory for one polaron is examined on the 1D discrete lattice described by the Holstein Hamiltonian. The latter is characterized by the electron hopping t, the phonon frequency ω_0 and the electronphonon coupling g. It is shown that the polaron localization (and translation) properties are contained in the electron propagator of one electron, intermittently added to the lattice, and/or in the phonon correlation function with one electron permanently present in the lattice. The order by order analysis in g/ω_0 shows that the expansion of the irreducible electron selfenergy corresponds to the expansion of the phonon correlation function, rather than of the irreducible phonon selfenergy. The range of polaronic correlations is determined in this way. For small t/ω_0 and already to the second order g/ω_0 small, the electronlattice correlation becomes very short ranged, i.e. the polaron is already localized to one site, although the overall translational symmetry remains unbroken. For large t/ω0, the second order result is meaningful up to large g/ω_0 ≈ (t/ω_0)^\frac14, where it becomes degenerate with the results for the large adiabatic Holstein polaron. This suggests that the translationally invariant perturbation theory crosses then over smoothly, without symmetry breaking, into the adiabatic, continuous quantum limit, as rigorously demonstrated in the companion paper. Thus the quantum theory of the large adiabatic Holstein polaron provides a simple, instructive example of the quantum crossover which replaces the behavior in the quantum critical point.
Item Type:  Article 

Keywords:  polaron, electronphonon coupling, Holstein model, symmetry breaking 
Date:  2005 
Subjects:  NATURAL SCIENCES > Physics 
Divisions:  Faculty of Science > Department of Physics 
Publisher:  Hrvatsko fizikalno društvo 
Depositing User:  Gordana Stubičan Ladešić 
Date Deposited:  15 Apr 2014 17:36 
Last Modified:  15 Apr 2014 17:36 
URI:  http://digre.pmf.unizg.hr/id/eprint/856 
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