Coherent-state ansatz for the Holstein polaron in one and two dimensions

The Holstein model often serves as an archetype for electron-phonon interactions and polaron formation in solids. However, precise descriptions of the Holstein polaron are difficult when the phonon frequency is small and the electron-phonon coupling is strong, due to the presence of many phonons in the ground state. We present a semi-analytical approximation that consists of a variational ansatz with clouds of phonons surrounding the electron in the form of coherent states. This becomes particularly simple and exact in the Lang-Firsov limit. We determine the domain of validity away from this limit, and further explore the improvement achieved with a removal of the requirement that the phonon clouds form coherent states. Both approximations work extremely well at strong coupling, and both work surprisingly well also at weak coupling. The coherent-state ansatz provides a simple and intuitive picture of the polaron ground-state wavefunction, and in addition predicts accurate values for the ground-state energy and effective mass.