Exact weak-coupling radius of the Holstein polaron in one, two, and three dimensions

Details Exact weak-coupling radius of the Holstein polaron in one, two, and three dimensions Exact weak-coupling radius of the Holstein polaron in one, two, and three dimensions

1998-08-31

arxiv.org/abs/cond-mat/9808348v1

Physics Letters A Vol. 254, 287 (1999)

Physics

Condensed Matter

Strongly Correlated Electrons

4 Pages, 2 figures

Scientific paper

10.1016/S0375-9601(99)00108-5

We apply weak-coupling perturbation theory to the Holstein molecular crystal model in order to compute an electron-phonon correlation function characterizing the shape and size of the polaron lattice distortion in one, two, and three dimensions. This correlation function is computed exactly to leading order in the electron-phonon coupling constant, permitting a complete description of correlations in any dimension for both isotropic and arbitrarily anisotropic cases. Using this exact result, the width of the polaron is characterized along arbitrary directions. The width of the polaron thus determined disagrees in every dimension with some well-known characterizations of polarons, signalling in particular the breakdown of the adiabatic approximation and the characterizations of self-trapping associated with it.

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