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

## TL;DR

This paper introduces a nonperturbative analytical method to study polaron-induced band renormalization in electron-phonon systems, accounting for both linear and quadratic couplings, and applies it to organic crystals like naphthalene.

## Contribution

It develops a novel, explicit analytical approach to analyze band narrowing due to electron-phonon interactions beyond linear coupling, applicable in strong-coupling regimes.

## Key findings

- Derived explicit analytical expressions for eigenvalue spectra.
- Demonstrated band narrowing as a function of temperature.
- Applied the model to naphthalene with ab initio coupling parameters.

## Abstract

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.