Single-polaron properties of the one-dimensional breathing-mode Hamiltonian

We investigate numerically various properties of the one-dimensional (1D) breathing-mode polaron. We use an extension of a variational scheme to compute the energies and wave functions of the two lowest-energy eigenstates for any momentum, as well as a scheme to compute directly the polaron’s Green’s function. We contrast these results with the results for the 1D Holstein polaron. In particular, we find that the crossover from a large to a small polaron is significantly sharper. Unlike for the Holstein model, at moderate and large couplings, the breathing-mode polaron dispersion has nonmonotonic dependence on the polaron momentum k. Neither of these aspects is revealed by a previous study based on the self-consistent Born approximation.