The Small Polaron Crossover: Role of Dimensionality

Details The Small Polaron Crossover: Role of Dimensionality The Small Polaron Crossover: Role of Dimensionality

1998-12-11

arxiv.org/abs/cond-mat/9812195v1

Physics

Condensed Matter

Strongly Correlated Electrons

4 pages, 3 figures. To appear in J. of Superconductivity (Proceedings Stripes98)

Scientific paper

The crossover from quasi free electron to small polaron in the Holstein model for a single electron is studied by means of both exact and self-consistent calculations in one dimension and on an infinite coordination lattice, in order to understand the role of dimensionality in such a crossover. We show that a small polaron ground-state occurs when both strong coupling ($\lambda>1$) and multiphonon ($\alpha^2 >1$) conditions are fulfilled leading to different relevant coupling constants ($\lambda$) in adiabatic and ($\alpha^2$) anti adiabatic region of the parameters space. We also show that the self-consistent calculations obtained by including the first electron-phonon vertex correction give accurate results in a sizeable region of the phase diagram well separated from the polaronic crossover.

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