Polarons, bipolarons and few-polaron states in the Peierls model of electron-phonon coupling

We consider the one-dimensional Peierls model of electron-phonon coupling describing the modulation of the electron hopping by phonons. We review recent results on single polarons and bipolarons, and extend our discussion to few-polaron states in the regime of competing phononic and electronic excitations. Single polarons experience a transition from weak coupling to strong coupling, while the Peierls coupling stabilitizes strongly bound yet very ligh bipolarons. Few polarons, however, experience higher order interactions that result in the formation of multipolaron bound states. In the anti-adiabatic limit of large phonon frequencies, we find that bipolarons are stable against phase separation. We discuss the relevance of these ideas to superconductivity in higher dimensions.