Green's and spectral functions of small Frohlich polaron

According to recent quantum Monte Carlo simulations, the small polaron theory is practically exact in a wide range of the long-range (Frohlich) electron-phonon coupling and adiabatic ratio. Applying Lang-Firsov transformation, we derive a single-particle Green's function describing the propagation of small Frohlich polaron. One- and two-dimensional spectral functions are studied by expanding Green's function perturbatively. Remarkably, the coherent spectral weight (Z) and effective mass (Z') renormalisation exponents are found to be different with Z' much greater than Z, which can explain a small coherent spectral weight and a relatively moderate mass enhancement in oxides.