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Exact results for the density of states and the ac conductivity of the spinless Holstein model at finite carrier density are obtained combining Lanczos and kernel polynomial methods.
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The cross over from low to high carrier densities in a many-polaron system is studied in the framework of the one-dimensional spinless Holstein model, using unbiased numerical methods. Combining a novel quantum Monte Carlo approach and exact diagonalization, accurate results for the single-particle spectrum and the electronic kinetic energy on fairly large systems are obtained. A detailed investigation of the quality of the Monte Carlo data is presented. In the physically most important adiabatic intermediate electron-phonon coupling regime, for which no analytical results are available, we observe a dissociation of polarons with increasing band filling, leading to normal metallic behavior, while for parameters favoring small polarons, no such density-driven changes occur. The present work points towards the inadequacy of single-polaron theories for a number of polaronic materials such as the manganites.
Optical conductivity of an interacting polaron gas is calculated within an extended random phase approximation which takes into account mixing of collective excitations of the electron gas with LO phonons. This mixing is important for the optical response of strongly polar crystals where the static dielectric constant is rather high: strontium titanate is the case. The present calculation sheds light on unexplained features of experimentally observed optical conductivity spectra in $n$-doped SrTiO$_{3}$. These features appear to be due to dynamic screening of the electron-electron interaction by polar optical phonons and hence do not require additional mechanisms for the explanation.
Polaron binding energy and effective mass are calculated in the fractional-dimensional space approach using the second-order perturbation theory. The effect of carrier density on the static screening correction of the electron-phonon interaction is calculated using the Hubbards local field factor. It is found that the effective mass and the binding energy both decrease with increase in doping.
The carrier-density dependence of the photoemission spectrum of the Holstein many-polaron model is studied using cluster perturbation theory combined with an improved cluster diagonalization by Chebychev expansion.
We present accurate results for optical conductivity of the three dimensional Frohlich polaron in all coupling regimes. The systematic-error free diagrammatic quantum Monte Carlo method is employed where the Feynman graphs for the momentum-momentum correlation function in imaginary time are summed up. The real-frequency optical conductivity is obtained by the analytic continuation with stochastic optimization. We compare numerical data with available perturbative and non-perturbative approaches to the optical conductivity and show that the picture of sharp resonances due to relaxed excited states in the strong coupling regime is ``washed outby large broadening of these states. As a result, the spectrum contains only a single-maximum broad peak with peculiar shape and a shoulder.
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