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We present a novel approach to electron-lattice interaction beyond thelinear-coupling regime. Based on the solution of a Holstein-Peierls-type model,we derive explicit analytical expressions for the eigenvalue spectrum of theHamiltonian, 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, theformalism also applies in the strong-coupling case. We apply it to the organiccrystal naphthalene, with the coupling strengths obtained by \textit{ab initio}calculations.

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