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Small polaron formation in many-particle states of the Hubbard-Holstein model: The one-dimensional case

Massimo Capone·Marco Grilli·Walter Stephan
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Abstract

We investigate polaron formation in a many-electron system in the presence of a local repulsion sufficiently strong to prevent local-bipolaron formation. Specifically, we consider a Hubbard-Holstein model of interacting electrons coupled to dispersionless phonons of frequency $ω_0$. Numerically solving the model in a small one-dimensional cluster, we find that in the nearly adiabatic case $ω_0 < t$, the necessary and sufficient condition for the polaronic regime to occur is that the energy gain in the atomic (i.e., extremely localized) regime ${\cal E}_{pol}$ overcomes the energy of the purely electronic system $ {\cal E}_{el}$. In the antiadiabatic case, $ω_0 > t$, polaron formation is instead driven by the condition of a large ionic displacement $g/ω_0 >1$ ($g$ being the electron-phonon coupling). Dynamical properties of the model in the weak and moderately strong coupling regimes are also analyzed.

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Massimo Capone, Marco Grilli, Walter Stephan. 1999-02-23. Small polaron formation in many-particle states of the Hubbard-Holstein model: The one-dimensional case. https://doi.org/10.1007/s100510051182

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