Polaron-induced band renormalization due to linear and quadratic electron-phonon coupling

We present a novel approach to electron-lattice interaction beyond the linear-coupling regime. Based on the solution of a Holstein-Peierls-type model, we derive explicit analytical expressions for the eigenvalue spectrum of the Hamiltonian, resulting in a narrowing of bands as a function of temperature. Our approach enables the intuitive interpretation in terms of quasiparticles, i.e. polaron bands and dressed-phonon frequencies. Being nonperturbative, the formalism also applies in the strong-coupling case. We apply it to the organic crystal naphthalene, with the coupling strengths obtained by \textit{ab initio} calculations.