Abstract
The phonon spectral function of the one-dimensional Holstein model is obtained withinweak-coupling and strong-coupling approximations based on analytical self-energycalculations. The characteristic excitations found in the limit of small charge-carrier densityare related to the known (electronic) spectral properties of Holstein polarons such as thepolaron band dispersion. Particular emphasis is laid on the different physics occurring inthe adiabatic and anti-adiabatic regimes, respectively. Comparison is made with a clusterapproach exploiting exact numerical results on small systems to yield an approximation forthe thermodynamic limit. This method, similar to cluster perturbation theory, confirms theanalytical findings, and also yields accurate results in the intermediate-coupling regime.
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